unification of infinite sets of terms schematized by primal grammars abstract infinite sets of terms appear frequently at different places in computer science on the other hand several practically oriented parts of logic and computer science require the manipulated objects to be finite or finitely representable schematizations present a suitable formalism to manipulate finitely infinite sets of terms since schematizations provide a different approach to solve the same kind of problems as constraints do they can be viewed as a new type of constraints the paper presents a new recurrent schematization called primal grammars the main idea behind the primal grammars is to use primitive recursion as the generating engine of infinite sets the evaluation of primal grammars is based on substitution and rewriting hence no particular semantics for them is necessary this fact allows also a natural integration of primal grammars into prolog into functional languages or into other rewrite based applications primal grammars have a decidable unification problem and the paper presents a unification algorithm for them that produces finite results this unification algorithm is proved sound and complete and it terminates for every input

finding explanations of inconsistency in multi context systems interlinking knowledge sources to enable information exchange is basic means to build enriched knowledge based systems which gains importance with the spread of the internet inconsistency however arises easily in such systems which is not least due to their heterogeneity but also due to their independent design this makes developing methods for consistency management of such systems a pressing issue an important aspect is that in many relevant cases the information at individual sources may not be amenable to change in order to resolve inconsistency like in case of autonomous management of the sources we thus aim at analyzing inconsistency of a system by means of the interlinking of sources and changes thereof more concretely we consider the powerful framework of multi context systems in which decentralized and heterogeneous system parts interact via possibly nonmonotonic bridge rules for information exchange nonmonotonicity and potential cyclic dependencies pose additional challenges that call for suitable methods of inconsistency analysis we thus provide two approaches for explaining inconsistency which both characterize inconsistency in terms of bridge rules but in different ways by pointing out rules which need to be altered for restoring consistency and by finding combinations of rules which cause inconsistency we show duality and modularity properties of these notions give precise complexity characterizations and provide algorithms for their computation which have been implemented in a prototype by means of so called hex programs our results provide a basis for inconsistency management in heterogeneous knowledge systems which different from and orthogonal to other works explicitly addresses the knowledge interlinks in order to restore consistency

an automata theoretic decision procedure for the propositional mu calculus the propositional mu calculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the propositional dynamic logic of fischer and ladner the infinite looping construct of streett and the game logic of parikh we give an elementary time decision procedure using a reduction to the emptiness problem for automata on infinite trees a small model theorem is obtained as a corollary

succinct representation of regular languages by boolean automata ii abstract boolean automata are a generalization of finite automata in the sense that the next state the result of the transition function given a state and a letter is not just a single state deterministic automata or a set of states nondeterministic automata but a boolean function of the states boolean automata accept precisely the regular languages also they correspond in a natural way to certain language equation involving complementation as well as to sequential networks in a previous note we showed that for every n 1 there exists a boolean automaton b n with n states such that the smallest deterministic automaton for the same language has 2 2 n states in the present note we will show a precisely attainable lower bound on the succinctness of representing regular languages by boolean automata namely we will show that for every n 1 there exists a reduced automaton d n with n states such that the smallest boolean automaton accepting the same language has also n states

optimal temporal logic control for deterministic transition systems with probabilistic penalties we consider an optimal control problem for a weighted deterministic transition system required to satisfy a constraint expressed as a linear temporal logic ltl formula over its labels by assuming that the executions of the system incur time varying penalties modeled as markov chains our goal is to minimize the expected average cumulative penalty incurred between consecutive satisfactions of a desired property using concepts from theoretical computer science we provide two solutions to this problem first we derive a provably correct optimal strategy within the class of strategies that do not exploit values of penalties sensed in real time second we show that by taking advantage of locally sensing the penalties we can construct heuristic strategies leading to lower collected penalty while still ensuring satisfaction of the ltl constraint we cannot guarantee optimality in the latter case we provide a user friendly implementation of the proposed algorithms and analysis of two case studies

ltl over integer periodicity constraints periodicity constraints are used in many logical formalisms in fragments of presburger ltl in calendar logics and in logics for access control to quote a few examples in the paper we introduce the logic pltlmod an extension of linear time temporal logic ltl with past time operators whose atomic formulae are defined from a first order constraint language dealing with periodicity although the underlying constraint language is a fragment of presburger arithmetic shown to admit a pspace complete satisfiability problem we establish that pltlmod model checking and satisfiability problems remain in pspace as plain ltl full presburger ltl is known to be highly undecidable this is particularly interesting for dealing with periodicity constraints since the language of pltlmod has a language more concise than existing languages and the temporalization of our first order language of periodicity constraints has the same worst case complexity as the underlying constraint language finally we show examples of introduction the quantification in the logical language that provide to pltlmod expspace complete problems as another application we establish that the equivalence problem for extended single string automata known to express the equality of time granularities is pspace complete by designing a reduction from qbf and by using our results for pltlmod

verification by augmented finitary abstraction the paper deals with the proof method of verification by finitary abstraction vfa which presents a feasible approach to the verification of the temporal properties of potentially infinite state reactive systems the method consists of a two step process by which in a first step the system and its temporal specification are jointly abstracted into a finite state system and a finite state specification the second step uses model checking to establish the validity of the abstracted property over the abstracted system the vfa method can be considered a viable alternative to verification by temporal deduction which up to now has been the main method generally applicable for verification of infinite state systems the paper presents a general recipe for the joint abstraction which is shown to be sound where soundness means that validity over the abstract system implies validity over the concrete original system to make the method applicable for the verification of liveness properties pure abstraction is sometimes no longer adequate we show that by augmenting the system by an appropriate and standardly constructible progress monitor we obtain an augmented system whose computations are essentially the same as the original system and which may now be abstracted while preserving the desired liveness properties we refer to the extended method as verification by augmented abstraction vaa we then proceed to show that the vaa method is sound and complete for proving all properties expressible by temporal logic including both safety and liveness completeness establishes that whenever the property is valid there exists a finitary abstraction which abstracts the system augmented by an appropriate progress monitor into a finite state system which validated the abstracted property

deciding full branching time logic in this paper the full branching time logic ctl is studied it has basic modalities consisting of a path quantifier either a for all paths of e for some path followed by an arbitrary linear time assertion composed of unrestricted combinations of the usual linear temporal operators f sometime g always x nexttime and u until it is shown that the problem of determining if a ctl formula is satisfiable in a structure generated by a binary relation is decidable in triple exponential time the decision procedure exploits the special structure of the finite state automata for linear temporal formulae which allows them to be determinized with only a single exponential blowup in size also the expressive power of tree automata is compared with that of ctl augmented by quantified auxillary propositions

adding nesting structure to words we propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items examples of data with such dual linear hierarchical structure include executions of structured programs annotated linguistic data and html xml documents nested words generalize both words and ordered trees and allow both word and tree operations we define nested word automata finite state acceptors for nested words and show that the resulting class of regular languages of nested words has all the appealing theoretical properties that the classical regular word languages enjoys deterministic nested word automata are as expressive as their nondeterministic counterparts the class is closed under union intersection complementation concatenation kleene prefixes and language homomorphisms membership emptiness language inclusion and language equivalence are all decidable and definability in monadic second order logic corresponds exactly to finite state recognizability we also consider regular languages of infinite nested words and show that the closure properties mso characterization and decidability of decision problems carry over the linear encodings of nested words give the class of visibly pushdown languages of words and this class lies between balanced languages and deterministic context free languages we argue that for algorithmic verification of structured programs instead of viewing the program as a context free language over words one should view it as a regular language of nested words or equivalently a visibly pushdown language and this would allow model checking of many properties such as stack inspection pre post conditions that are not expressible in existing specification logics we also study the relationship between ordered trees and nested words and the corresponding automata while the analysis complexity of nested word automata is the same as that of classical tree automata they combine both bottom up and top down traversals and enjoy expressiveness and succinctness benefits over tree automata

formally reasoning about quality in recent years there has been a growing need and interest in formally reasoning about the quality of software and hardware systems as opposed to traditional verification in which one considers the question of whether a system satisfies a given specification or not reasoning about quality addresses the question of how well the system satisfies the specification we distinguish between two approaches to specifying quality the first propositional quality extends the specification formalism with propositional quality operators which prioritize and weight different satisfaction possibilities the second temporal quality refines the eventually operators of the specification formalism with discounting operators whose semantics takes into an account the delay incurred in their satisfaction in this article we introduce two quantitative extensions of linear temporal logic ltl one by propositional quality operators and one by discounting operators in both logics the satisfaction value of a specification is a number in 0 1 which describes the quality of the satisfaction we demonstrate the usefulness of both extensions and study the decidability and complexity of the decision and search problems for them as well as for extensions of ltl that combine both types of operators

undecidability of subsumption in nikl abstract subsumption determining whether one concept is more general than another is known to be np hard for all reasonably expressive terminological logics but up to now the decidability of subsumption for terminological logics used in current knowledge representation systems such as nikl remained unknown this paper shows that subsumption in the terminological logic of nikl is undecidable and thus that there are no complete algorithms for subsumption or classification in nikl

propositional dynamic logic of flowcharts following a suggestion of pratt we consider propositional dynamic logic in which programs are nondeterministic finite automata over atomic programs and tests i e flowcharts rather than regular expressions while the resulting version of pdl call it apdl is clearly equivalent in expressive power to pdl it is also in the worst case exponentially more succinct in particular deciding its validity problem by reducing it to that of pdl leads to a double exponential time procedure although pdl itself is decidable in exponential time we present an elementary combined proof of the completeness of a simple axiom system for apdl and decidability of the validity problem in exponential time the results are thus stronger than those for pdl since pdl can be encoded in apdl with no additional cost and the proofs simpler since induction on the structure of programs is virtually eliminated our axiom system for apdl relates to the pdl system just as floyd s proof method for partial correctness relates to hoare s

an automata theoretic approach to constraint ltl we consider an extension of linear time temporal logic ltl with constraints interpreted over a concrete domain we use a new automata theoretic technique to show pspace decidability of the logic for the constraint systems z and n along the way we give an automata theoretic proof of a result of balbiani and condotta when the constraint system satisfies the completion property our decision procedures extend easily to handle extensions of the logic with past time operators and constants as well as an extension of the temporal language itself to monadic second order logic finally we show that the logic becomes undecidable when one considers constraint systems that allow a counting mechanism

e connections of abstract description systems combining knowledge representation and reasoning formalisms is an important and challenging task it is important because non trivial ai applications often comprise different aspects of the world thus requiring suitable combinations of available formalisms modeling each of these aspects it is challenging because the computational behavior of the resulting hybrids is often much worse than the behavior of their components in this paper we propose a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable and which nonetheless allows non trivial interactions between the combined components the new method called e connection is defined in terms of abstract description systems adss a common generalization of description logics many logics of time and space as well as modal and epistemic logics the basic idea of e connections is that the interpretation domains of n combined systems are disjoint and that these domains are connected by means of n ary link relations we define several natural variants of e connections and study in depth the transfer of decidability from the component systems to their e connections

signal separation using fractional sampling in multiuser communications described is a decorrelating filter that separates signals in a multiuser environment by relying on the relative delays to be sufficiently distinct the input signal is fractionally sampled to allow for the differentiation of the user delays both zero forcing and minimum mean square error versions of this filter are derived and probability of error expressions are given the algorithm successfully separates unknown digital signals by using the known received pulse shapes and the symbol rate a delay division multiple access ddma scheme based on this signal decorrelator is proposed that will allow signals to be transmitted without spreading the signal spectrum it is shown that in a noisy environment the signal to noise ratio penalty for ddma can be severe yet the bandwidth advantage is very pronounced compared to spread spectrum systems and is similar to other bandwidth efficient schemes the performance of a code division multiple access cdma system using this signal decorrelator is also given the decorrelator can be used as a blind multiuser detector or as a preprocessor to enhance the performance of a cdma system

batch size effects in the analysis of simulation output batching is a commonly used method for calculating confidence intervals on the mean of a sequence of correlated observations arising from a simulation experiment several recent papers have considered the effect of using batch sizes too small to satisfy assumptions of normality and or independence and the resulting incorrect probabilities of the confidence interval covering the mean this paper quantifies the effects of using batch sizes larger than necessary to satisfy normality and independence assumptions these effects include 1 correct probability of covering the mean 2 an increase in expected half length 3 an increase in the standard deviation and coefficient of variation of the half length and 4 an increase in the probability of covering points not equal to the mean for any sample size and independent and normal batch means the results are 1 the effects of less than 10 batches are large and the effects of more than 30 batches small and 2 additional batches have lesser effects on

qualitative analysis of gene regulatory networks by temporal logic in this article we propose a novel formalism to model and analyse gene regulatory networks using a well established formal verification technique we model the possible behaviours of networks by logical formulae in linear temporal logic ltl by checking the satisfiability of ltl it is possible to check whether some or all behaviours satisfy a given biological property which is difficult in quantitative analyses such as the ordinary differential equation approach owing to the complexity of ltl satisfiability checking analysis of large networks is generally intractable in this method to mitigate this computational difficulty we developed two methods one is a modular checking method where we divide a network into subnetworks check them individually and then integrate them the other is an approximate analysis method in which we specify behaviours in simpler formulae which compress or expand the possible behaviours of networks in the approximate method we focused on network motifs and presented approximate specifications for them we confirmed by experiments that both methods improved the analysis of large networks we propose a novel qualitative method for analysing gene networks based on formal verification technique behaviours and properties of networks are described in temporal logic formulae by checking satisfiability of the formula we can analyse properties of the network to improve the efficiency of analysis we developed the modular and approximate method

asynchronous knowledge with hidden actions in the situation calculus abstract we present a powerful new account of multi agent knowledge in the situation calculus and an automated reasoning procedure for knowledge queries existing accounts of epistemic reasoning in the situation calculus require that whenever an action occurs all agents know that an action has occurred this demands a level of synchronicity that is unreasonable in many multi agent domains in asynchronous domains each agent s knowledge must instead account for arbitrarily long sequences of hidden actions by using a persistence condition meta operator to augment traditional regression techniques we show how agents can reason about their own knowledge using only their internal history of observations rather than requiring a full history of the world the result is a more robust and flexible account of knowledge in the situation calculus suitable for asynchronous partially observable multi agent domains

a polynomial space construction of tree like models for logics with local chains of modal connectives the la logics logics with local agreement are polymodal logics defined semantically such that at any world of a model the sets of successors for the different accessibility relations can be linearly ordered and the accessibility relations are equivalence relations in a previous work we have shown that every la logic defined with a finite set of modal indices has an np complete satisfiability problem in this paper we introduce a class of la logics with a countably infinite set of modal indices and we show that the satisfiability problem is pspace complete for every logic of such a class the upper bound is shown by exhibiting a tree structure of the models this allows us to establish a surprising correspondence between the modal depth of formulae and the number of occurrences of distinct modal connectives more importantly as a consequence we can show the pspace completeness of gargov s logic dalla and nakamura s logic lgm restricted to modal indices that are rational numbers for which the computational complexity characterization has been open until now these logics are known to belong to the class of information logics and fuzzy modal logics respectively

forgetting in multi agent modal logics abstract in the past decades forgetting has been investigated for many logics and has found many applications in knowledge representation and reasoning in this paper we study forgetting in multi agent modal logics we adopt the semantic definition of existential bisimulation quantifiers as that of forgetting we resort to canonical formulas of modal logics introduced by moss an arbitrary modal formula is equivalent to the disjunction of a unique set of satisfiable canonical formulas we show that for the logics of k n d n t n k 45 n kd 45 n and s 5 n the result of forgetting an atom from a satisfiable canonical formula can be computed by simply substituting the literals of the atom with thus we show that these logics are closed under forgetting and hence have uniform interpolation finally we generalize the above results to include common knowledge of propositional formulas

on the relative expressiveness of description logics and predicate logics abstract it is natural to view concept and role definitions in description logics as expressing monadic and dyadic predicates in predicate calculus we show that the descriptions built using the constructors usually considered in the dl literature are characterized exactly as the predicates definable by formulas in tl3 the subset of first order predicate calculus with monadic and dyadic predicates which allows only three variable symbols in order to handle number bounds we allow numeric quantifiers and for transitive closure of roles we use infinitary disjunction using previous results in the literature concerning languages with limited numbers of variables we get as corollaries the existence of formulas of fopc which cannot be expressed as descriptions we also show that by omitting role composition descriptions express exactly the formulas in tl2 which is known to be decidable

process logic with regular formulas the paper proposes an extension rpl of the process logic pl of harel kozen and parikh 1980 the pl formula operators f and suf are replaced by the operators chop and slice corresponding to kleene s regular operators and thus enabling formulas to express regular sets of paths the main result is that in expressive power pl rpl the hard part being in showing that pl rpl it is argued that this version of pl comes closer to the desired goal of a natural and powerful yet decidable logic for reasoning about the ongoing behavior of programs

looping vs repeating in dynamic logic two extensions of propositional dynamic logic for dealing with infinite computations lpdl and rpdl are compared in expressive power the first is obtained by adding the assertion loop for any program meaning contains an infinite computation and the second by adding repeat meaning can be repeated indefinitely while repeat can be used to encode loop and hence lpdl rpdl it is shown here that the converse fails thus lpdl

the verification and control of interacting similar discrete event systems this paper explore issues related to the control and verification of similar module systems in the discrete event systems framework similar module systems are distributed systems comprised of subsystem modules that exhibit isomorphic local behavior coordinated on global event occurrences when given a global model of these systems it is shown how to decompose the global model into the component subsystems in polynomial time it is also shown how to perform various verification tasks for these interacting systems while mitigating common state explosion difficulties by taking advantage of the special similar module system structure control properties of the similar module systems are also discussed it is assumed that the local modules are supervised by exactly one local controller and the controllers enforce the same local control policy necessary and sufficient conditions for achieving local and global control specifications in this setting are identified

hidden protocols modifying our expectations in an evolving world when agents know a protocol this leads them to have expectations about future observations agents can update their knowledge by matching their actual observations with the expected ones they eliminate states where they do not match in this paper we study how agents perceive protocols that are not commonly known and propose a semantics driven logical framework to reason about knowledge in such scenarios in particular we introduce the notion of epistemic expectation models and a propositional dynamic logic style epistemic logic for reasoning about knowledge via matching email protected expectations to their observations it is shown how epistemic expectation models can be obtained from epistemic protocols furthermore a characterization is presented of the effective equivalence of epistemic protocols we introduce a new logic that incorporates updates of protocols and that can model reasoning about knowledge and observations finally the framework is extended to incorporate fact changing actions and a worked out example is given

a logic for reasoning about counterfactual emotions the aim of this work is to propose a logical framework for the specification of cognitive emotions that are based on counterfactual reasoning about agents choices the prototypical counterfactual emotion is regret in order to meet this objective we exploit the well known stit logic belnap et al 2001 9 horty 2001 30 horty and belnap 1995 31 stit logic has been proposed in the domain of formal philosophy in the nineties and more recently it has been imported into the field of theoretical computer science where its formal relationships with other logics for multi agent systems such as atl and coalition logic cl have been studied stit is a very suitable formalism to reason about choices and capabilities of agents and groups of agents unfortunately the version of stit with agents and groups has been recently proved to be undecidable and not finitely axiomatizable in this work we study a decidable and finitely axiomatizable fragment of stit with agents and groups which is sufficiently expressive for our purpose of formalizing counterfactual emotions we call dfstit our stit fragment after having extended dfstit with knowledge modalities in the second part of article we exploit it in order to formalize four types of counterfactual emotions regret rejoicing disappointment and elation at the end of the article we present an application of our formalization of counterfactual emotions to a concrete example

new user identification in a cdma system we present three detector estimators des which allow multiuser detection and parameter estimation without a side channel in a dynamic asynchronous code division multiple access cdma system in which users are entering and leaving the system these des optimally detect a new user given only the chip rate and the spreading factor of the new user two of these des the maximum likelihood detector estimator mlde and the generalized maximum likelihood detector estimator gmlde produce maximum likelihood estimates of the new user s signature sequence delay and amplitude which are then incorporated into a multiuser detector the third de the cyclic detector estimator cde is the most computationally efficient of the three processors this de detects the new user by testing for cyclostationarity and then uses suboptimal schemes to estimate the new user s signature sequence delay and amplitude simulations indicate that all three des reliably detect a new user for an e sub s spl sigma sup 2 symbol energy to noise ratio of 5 db the mlde and gmlde produce signature sequence and delay estimates with probability of error less than 0 07 for an e sub s spl sigma sup 2 of 10 db and the cde produces signature sequence and delay estimates with probability of error less than 0 13 for an e sub s spl sigma sup 2 of 15 db

coping with selfish on going behaviors a rational and selfish environment may have an incentive to cheat the system it interacts with cheating the system amounts to reporting a stream of inputs that is different from the one corresponding to the real behavior of the environment the system may cope with cheating by charging penalties to cheats it detects in this paper we formalize this setting by means of weighted automata and their resilience to selfish environments automata have proven to be a successful formalism for modeling the on going interaction between a system and its environment in particular weighted finite automata wfas which assign a cost to each input word are useful in modeling an interaction that has a quantitative outcome consider a wfa a over the alphabet s at each moment in time the environment may cheat a by reporting a letter different from the one it actually generates a penalty function h email protected r 0 maps each possible false report to a penalty charged whenever the false report is detected a detection probability function p email protected 0 1 gives the probability of detecting each false report we say that a is h p resilient to cheating if ensures that the minimal expected cost of an input word is achieved with no cheating thus a rational environment has no incentive to cheat a we study the basic problems arising in the analysis of this setting in particular we consider the problem of deciding whether a given wfa a is h p resilient with respect to a given penalty function h and a detection probability function p and the problem of achieving resilience with minimum resources namely given a and h finding the minimal with respect to s s h s s p s s detection probability function p such that a is h p resilient while for general wfas both problems are shown to be pspace hard we present polynomial time algorithms for deterministic wfas

an epistemic operator for description logics abstract description logics also called terminological logics or concept languages are fragments of first order logic that provide a formal account of the basic features of frame based systems however there are aspects of frame based systems such as nonmonotonic reasoning and procedural rules that cannot be characterized in a standard first order framework such features are needed for real applications and a clear understanding of the logic underlying them is necessary for principled implementations we show how description logics enriched with an epistemic operator can formalize such aspects the logic obtained is a fragment of a first order nonmonotonic modal logic we show that the epistemic operator formalizes procedural rules as provided in many knowledge representation systems and enables sophisticated query formulation including various forms of closed world reasoning we provide an effective procedure for answering epistemic queries posed to a knowledge base expressed in a description logic and extend this procedure in order to deal with rules we also address the computational complexity of reasoning with the epistemic operator identifying cases in which an appropriate use of the epistemic operator can help in decreasing the complexity of reasoning

the propositional dynamic logic of deterministic well structured programs abstract we consider a restricted propositional dynamic logic strict deterministic propositional dynamic logic sdpdl which is appropriate for reasoning about deterministic well structured programs in contrast to pdl for which the validity problem is known to be complete in deterministic exponential time the validity problem for sdpdl is shown to be polynomial space complete we also show that sdpdl is less expressive than pdl and give a complete axiomatization for it the results rely on structure theorems for models of satisfiable sdpdl formulas and the proofs give insight into the effects of nondeterminism on intractability and expressiveness in program logics

infinite games with finite knowledge gaps infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable unless the information is hierarchically ordered among the players we identify a class of games for which joint winning strategies can be constructed effectively without restricting the direction of information flow instead our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play we show that it is decidable whether a given game satisfies the condition and prove tight complexity bounds for the strategy synthesis problem under regular winning conditions given by deterministic parity automata

alternating finite automata on ω words abstract alternating finite automata on words are introduced as an extension of nondeterministic finite automata which process infinite sequences of symbols the classes of languages defined by alternating finite automata are investigated and characterized under four types of acceptance conditions it is shown that for one type of acceptance condition alternation increases the power in comparison with nondeterminism and for other three acceptance conditions nondeterministic finite automata on words have the same power as alternating ones

knowledge probability and adversaries what should it mean for an agent to know or believe an assertion is true with probability 9 99 different papers 2 6 15 give different answers choosing to use quite different probability spaces when computing the probability that an agent assigns to an event we show that each choice can be understood in terms of a betting game this betting game itself can be understood in terms of three types of adversaries influencing three different aspects of the game the first selects the outcome of all nondeterministic choices in the system the second represents the knowledge of the agent s opponent in the betting game this is the key place the papers mentioned above differ and the third is needed in asynchronous systems to choose the time the bet is placed we illustrate the need for considering all three types of adversaries with a number of examples given a class of adversaries we show how to assign probability spaces to agents in a way most appropriate for that class where most appropriate is made precise in terms of this betting game we conclude by showing how different assignments of probability spaces corresponding to different opponents yield different levels of guarantees in probabilistic coordinated attack

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

joint signal detection and parameter estimation in multiuser communications the problem of simultaneously detecting the information bits and estimating signal amplitudes and phases in a k user asynchronous direct sequence spread spectrum multiple access communication system is addressed the joint maximum likelihood ml estimator has a computational complexity that is exponential in the total number of bits transmitted and thus does not represent a practical solution to the problem an estimator that combines a suboptimum tree search algorithm with a recursive least squares estimator of complex signal amplitude is considered the complexity of this estimator is o k sup 2 computations per decoded bit and its performance is very close to that of the joint ml receiver this receiver has the advantage that the transmitted signal powers and phases are extracted from the received signal in an adaptive fashion without using a test sequence

reasoning about knowledge and probability we provide a model for reasoning about knowledge and probability together we allow explicit mention of probabilities in formulas so that our language has formulas that essentially say according to agent i formula holds with probability at least b the language is powerful enough to allow reasoning about higher order probabilities as well as allowing explicit comparisons of the probabilities an agent places on distinct events we present a general framework for interpreting such formulas and consider various properties that might hold of the interrelationship between agents probability assignments at different states we provide a complete axiomatization for reasoning about knowledge and probability prove a small model property and obtain decision procedures

an automata theoretic approach to branching time model checking translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear time model checking and for obtaining many extensions and improvements to this verification method on the other hand for branching temporal logic automata theoretic techniques have long been thought to introduce an exponential penalty making them essentially useless for model checking recently bernholtz and grumberg 1993 have shown that this exponential penalty can be avoided though they did not match the linear complexity of non automata theoretic algorithms in this paper we show that alternating tree automata are the key to a comprehensive automata theoretic framework for branching temporal logics not only can they be used to obtain optimal decision procedures as was shown by muller et al but as we show here they also make it possible to derive optimal model checking algorithms moreover the simple combinatorial structure that emerges from the automata theoretic approach opens up new possibilities for the implementation of branching time model checking and has enabled us to derive improved space complexity bounds for this long standing problem

a guide to completeness and complexity for modal logics of knowledge and belief abstract we review and re examine possible worlds semantics for propositional logics of knowledge and belief with three particular points of emphasis 1 we show how general techniques for finding decision procedures and complete axiomatizations apply to models for knowledge and belief 2 we show how sensitive the difficulty of the decision procedure is to such issues as the choice of modal operators and the axiom system and 3 we discuss how notions of common knowledge and distributed knowledge among a group of agents fit into the possible worlds framework as far as complexity is concerned we show among other results that while the problem of deciding satisfiability of an s5 formula with one agent is np complete the problem for many agents is pspace complete adding a distributed knowledge operator does not change the complexity but once a common knowledge operator is added to the language the problem becomes complete for exponential time

possibilistic reasoning a mini survey and uniform semantics abstract in this paper we survey some quantitative and qualitative approaches to uncertainty management based on possibility theory and present a logical framework to integrate them the semantics of the logic is based on the dempster s rule of conditioning for possibility theory it is then shown that classical modal logic conditional logic possibilistic logic quantitative modal logic and qualitative possibilistic logic are all sublogics of the presented logical framework in this way we can formalize and generalize some well known results about possibilistic reasoning in a uniform semantics moreover our uniform framework is applicable to nonmonotonic reasoning approximate consequence relation formulation and partial consistency handling

the complementation problem for bu chi automata with applications to temporal logic the problem of complementing buchi automata arises when developing procedures for temporal logics of programs unfortunately previously known constructions for complementing buchi automata involve a doubly exponential blow up in the size of the automaton we present a construction that involves only an exponential blow up we use this construction to prove a polynomial space upper bound for the propositional temporal logic of regular events and to prove a complexity hierarchy result for quantified propositional temporal logic

the alternation hierarchy in fixpoint logic with chop is strict too fixpoint logic with chop extends the modal calculus with a sequential composition operator which results in an increase in expressive power we develop a game theoretic characterisation of its model checking problem and use these games to show that the alternation hierarchy in this logic is strict the structure of this result follows the lines of arnold s proof showing that the alternation hierarchy in the modal calculus is strict over the class of binary trees

combining deduction and model checking into tableaux and algorithms for converse pdl this paper presents a prefixed tableaux calculus for propositional dynamic logic with converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for calculus we prove the correctness and completeness of the calculus and illustrate its features we also discuss the transformation of the tableaux method naively nexptime into an exptime algorithm

model checking of linear time properties in multi valued systems abstract in this paper we study the model checking problem of linear time properties in multi valued systems safety properties invariant properties liveness properties persistence and dual persistence properties in multi valued logic systems are introduced some algorithms related to the above multi valued linear time properties are discussed the verification of multi valued regular safety properties and multi valued regular properties using lattice valued automata are thoroughly studied since the law of non contradiction i e a a 0 and the law of excluded middle i e a a 1 do not hold in multi valued logic the linear time properties introduced in this paper have new forms compared to those in classical logic compared to those classical model checking methods our methods to multi valued model checking are accordingly more direct we give an algorithm for showing ts p for a model ts and a linear time property p which proceeds by directly checking the inclusion traces ts p instead of t r a c e s t s p a new form of multi valued model checking with membership degree is also introduced in particular we show that multi valued model checking can be reduced to classical model checking the related verification algorithms are also presented some illustrative examples and a case study are also provided

optimum multiuser asymptotic efficiency the degradation in bit error rate due to the presence of multiple access interference in a white gaussian channel can be measured by the multiuser asymptotic efficiency defined as the ratio between the snr required to achieve the same uncoded bit error rate in the absence of interfering users and the actual snr in this paper the asymptotic efficiency of the optimum multiuser demodulator a bank of matched filters followed by a viterbi algorithm is investigated and compared to that of the conventional single user matched filter receiver the computation of the optimum asymptotic efficiency of any given user is equivalent to the minimization of the euclidean distance between any pair of multiuser signals which differ in at least one of the symbols of that user it is shown that the optimum multiuser efficiency of asynchronous systems is nonzero with probability 1 and therefore the optimum demodulator does not become multiple access limited in contrast to the single user receiver a class of signal constellations with moderate cross correlation requirements is shown to achieve unit optimum multiuser efficiencies and hence to be equivalent to orthogonal signal sets from the viewpoint of performance of the optimum multiuser detector

classifying regular languages by a split game in this paper we introduce the split game a variant of the ehrenfeucht fraisse game from logic which is useful for analyzing the expressive power of classes of generalized regular expressions an extension of the split game to generalized w regular expressions is also established to gain insight into how the split game can be applied to attack the long standing generalized star height 2 problem we propose and solve the omega power problem a similar but tractable problem in the context of w languages namely we show that omega powers together with boolean combinations and concatenations are not sufficient to express the class of w regular languages

a nonstandard approach to the logical omniscience problem abstract we introduce a new approach to dealing with the well known logical omniscience problem in epistemic logic instead of taking possible worlds where each world is a model of classical propositional logic we take possible worlds which are models of a nonstandard propositional logic we call npl which is somewhat related to relevance logic this approach gives new insights into the logic of implicit and explicit belief considered by levesque and lakemeyer in particular we show that in a precise sense agents in the structures considered by levesque and lakemeyer are perfect reasoners in npl

a new combination procedure for the word problem that generalizes fusion decidability results in modal logics previous results for combining decision procedures for the word problem in the non disjoint case do not apply to equational theories induced by modal logics which are not disjoint for sharing the theory of boolean algebras conversely decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand and thus do not generalize to other types of equational theories in this paper we present a new approach for combining decision procedures for the word problem in the non disjoint case that applies to equational theories induced by modal logics but is not restricted to them the known fusion decidability results for modal logics are instances of our approach however even for equational theories induced by modal logics our results are more general since they are not restricted to so called normal modal logics

the effect of bounding the number of primitive propositions and the depth of nesting on the complexity of modal logic abstract a well known result of ladner says that the satisfiability problem for k45 kd45 and s5 is np complete this result implicitly assumes that there are infinitely many primitive propositions in the language it is easy to see that the satisfiability problem for these logics becomes linear time if there are only finitely many primitive propositions in the language by way of contrast we show that the pspace completeness results of ladner and halpern and moses hold for the modal logics k n t n s4 n n 1 and k45 n kd45 n s5 n n 2 even if there is only one primitive proposition in the language we go on to examine the effect on complexity of bounding the depth of nesting of modal operators if we restrict to finite nesting then the satisfiability problem is np complete for all the modal logics considered but s4 if we then further restrict the language to having only finitely many primitive propositions the complexity goes down to linear time in all cases

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

relevance from an epistemic perspective abstract in this paper we study relevance relations in the context of prepositional logical theories and subject matters or topics of interest which we take to be sets of atomic propositions in particular we are interested in answering questions like the following when is a sentence or theory relevant to a subject matter or when is a topic relevant to another topic or sentence given some background theory relevance is studied from a subjective or epistemic point of view that is we try to capture relevance relations from an agent s point of view relative to his or her deductive capabilities for this purpose we start out with the definition of regular belief which covers a wide range of belief models from the very weak to those closed under classical logical implication in the paper we consider one example from each of the extremes which are called explicit and implicit belief respectively we define a notion of prime implicates which applies to all models of regular belief and which has its usual meaning under implicit belief prime implicates turn out to be the right primitive from which all definitions of relevance are derived among the main technical contributions is a detailed comparison between relevance under implicit belief and three other approaches in the literature this investigation reveals that all four share a lot of common ground even though some have very different starting points we also study the complexity of determining relevance relations for implicit as well as explicit belief while intractability obtains often but not always for implicit belief the analogous problems for explicit belief are almost always tractable

axiomatising extended computation tree logic we present a sound and complete axiomatisation for extended computation tree logic this language extends the standard computation tree logic ctl by allowing path formulae to be expressed in linear time mu calculus instead of linear time temporal logic the main novelties in the current paper are an inference rule in the axiom system reflecting the limit closure of paths a new strongly aconjunctive deterministic normal form for formulae and the way the completeness proof takes advantage of techniques provided by automata theory

accepting conditions for automata on ω languages abstract in this paper we study the languages accepted by finite automata under a new type of accepting conditions which are based on whether the automaton enters all of its accepting states infinitely many times or not we investigate the classes of languages defined thereby in relation to other well known subclasses of the class of regular languages

on the decidability and complexity of reasoning about only knowing abstract we study reasoning in levesque s logic of only knowing in particular we first prove that extending a decidable subset of first order logic with the ability of reasoning about only knowing preserves decidability of reasoning as long as quantifying in is not allowed in the language and define a general method for reasoning about only knowing in such a case then we show that the problem of reasoning about only knowing in the propositional case lies at the second level of the polynomial hierarchy thus it is as hard as reasoning in the majority of propositional formalisms for nonmonotonic reasoning like default logic circumscription and autoepistemic logic and it is easier than reasoning in propositional formalisms based on the minimal knowledge paradigm which is strictly related to the notion of only knowing finally we identify a syntactic restriction in which reasoning about only knowing is easier than in the general propositional case and provide a specialized deduction method for such a restricted setting

complexity and succinctness issues for linear time hybrid logics full linear time hybrid logic hl is a non elementary and equally expressive extension of standard ltl past obtained by adding the well known binder operators 7 and we investigate complexity and succinctness issues for hl in terms of the number of variables and nesting depth of binder modalities first we present direct automata theoretic decision procedures for satisfiability and model checking of hl which require space of exponential height equal to the nesting depth of the binder modalities the proposed algorithms are proved to be asymptotically optimal by providing matching lower bounds second we show that for the one variable fragment of hl the considered problems are elementary and precisely expspace complete finally we show that for all 0 h

all i know a study in autoepistemic logic abstract current approaches to formalizing nonmonotonic reasoning using logics of belief require the definition of new metalogical properties over sets of sentences this research attempts to show how some of these patterns of reasoning can be captured using only the classical notions of logic satisfiability validity implication this is done by extending a logic of belief so that it is possible to say that only a certain proposition or finite set of them is believed this research also extends previous approaches to handle quantifiers and equality provides a semantic account of certain types of nonmonotonicity and through a simple proof theory allows formal derivations to be generated

model checking of linear time properties based on possibility measure using possibility measure we study model checking of linear time properties in possibilistic kripke structures first the notion of possibilistic kripke structures and the related possibility measure are introduced and then model checking of reachability and repeated reachability linear time properties in finite possibilistic kripke structures are studied standard safety properties and regular properties in possibilistic kripke structures are introduced the verification of regular safety properties and regular properties using finite automata are thoroughly studied it has been shown that the verification of regular safety properties and regular properties in a finite possibilistic kripke structure can be transformed into the verification of reachability properties and repeated reachability properties in the product possibilistic kripke structure that is introduced in this paper several examples are given to illustrate the methods that are presented in this paper

possible world semantics and autoepistemic reasoning abstract the possible world semantics of modal logic has been employed to study the nonmonotonic reasoning formalism moore s autoepistemic logic only kripke structure which is also known as a standard model has been used to represent the autoepistemic expansions of modal theories here we argue that the mode of autoepistemic reasoning which is formalized by autoepistemic logic is not necessarily associated with a standard model another model of the possible world semantics the minimal model is helpful in knowledge representation and belief reasoning in particular the minimal model can be used as a structure to represent all the autoepistemic expansions of a modal theory we extend the minimal model with standard model to deal with both knowledge and belief and introduce a null value called unknown to provide a refined model for knowledge and belief we also present a notion of epistemic base of basic sentences to identify the possible worlds in a minimal model by reformulating moore s autoepistemic logic with respect to epistemic base some reasonable modal theories that do not have any autoepistemic expansion will have generalized autoepistemic expansions

verification of qualitative z constraints we introduce an ltl like logic with atomic formulae built over a constraint language interpreting variables in z the constraint language includes periodicity constraints and comparison constraints of the form x y and x

an elementary proof of the completeness of pdl abstract we give an elementary proof of the completeness of the segerberg axions for propositional dynamic logic

attributive concept descriptions with complements abstract we investigate the consequences of adding unions and complements to attributive concept descriptions employed in terminological knowledge representation languages it is shown that deciding coherence and subsumption of such descriptions are pspace complete problems that can be decided with linear space

multivariate batch means and control variates we consider applying the nonoverlapping batch means output analysis method in conjunction with the control variate variance reduction technique to estimate a steady state multivariate mean vector the effects of the number of batches and the number of control variates on the multivariate point and region estimators and the univariate point and interval estimators are considered the results are experiment analysis guidelines in terms of an appropriate range of the number of batches to choose as a function of the number of responses and control variates the results have implications for terminating simulations as well

exp time tableaux for alc abstract the last years have seen two major advances in knowledge representation and reasoning first many interesting problems ranging from semi structured data to linguistics were shown to be expressible in logics whose main deductive problems are exptime complete second experiments in automated reasoning have substantially broadened the meaning of practical tractability instances of realistic size for pspace complete problems are now within reach for implemented systems still there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems indeed the algorithms based on tree automata which are used to prove exptime completeness require exponential time and space even in simple cases on the other hand current algorithms based on tableau methods can take advantage of such cases but require double exponential time in the worst case we propose a tableau calculus for the description logic alc for checking the satisfiability of a concept with respect to a tbox with general axioms and transform it into the first simple tableau based decision procedure working in single exponential time to guarantee the ease of implementation we also discuss the effects that optimizations propositional backjumping simplification semantic branching etc might have on our complexity result and introduce a few optimizations ourselves

reasoning about common knowledge with infinitely many agents complete axiomatizations and exponential time decision procedures are provided for reasoning about knowledge and common knowledge when there are infinitely many agents the results show that reasoning about knowledge and common knowledge with infinitely many agents is no harder than when there are finitely many agents provided that we can check the cardinality of certain set differences g g where g and g are sets of agents since our complexity results are independent of the cardinality of the sets g involved they represent improvements over the previous results even when the sets of agents involved are finite moreover our results make clear the extent to which issues of complexity and completeness depend on how the sets of agents involved are represented

propositional dynamic logic of looping and converse is elementarily decidable propositional dynamic logic is a formal system for reasoning about the before after behavior of regular program schemes an extension of propositional dynamic logic which includes both an infinite looping construct and a converse or backtracking construct is considered and it is proved that the satisfiability problem for this logic is elementarily decidable in order to establish this result deterministic two way automata on infinite trees are defined and it is shown how they can be simulated by nondeterministic one way automata the satisfiability problem for propositional dynamic logic of looping and converse is then reduced to the emptiness problem for these two way automata

on the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent s rational beliefs on gradable propositions it has recently been shown that in the same way as autoepistemic logic generalizes answer set programming fuzzy autoepistemic logic generalizes fuzzy answer set programming as well besides being related to answer set programming autoepistemic logic is also closely related to several modal logics to investigate whether a similar relationship holds in a fuzzy logical setting we firstly generalize the main modal logics for belief to the setting of finitely valued ukasiewicz logic with truth constants k c and secondly we relate them with fuzzy autoepistemic logics moreover we show that the problem of satisfiability checking in these logics is np complete finally we generalize levesque s results on stable expansions belief sets and only knowing operators to our setting and provide a complete axiomatization for a logic of only knowing in the k c framework

the complexity of concept languages abstract a basic feature of terminological knowledge representation systems is to represent knowledge by means of taxonomies here called terminologies and to provide a specialized reasoning engine to do inferences on these structures the taxonomy is built through a representation language called a concept language or description logic which is given a well defined set theoretic semantics the efficiency of reasoning has often been advocated as a primary motivation for the use of such systems the main contributions of the paper are 1 a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages 2 algorithms for these inferences that comply with the worst case complexity of the reasoning task they perform

ω regular languages are testable with a constant number of queries we continue the study of combinatorial property testing for a property an e test for for 0 0 we describe an algorithm that gets as input an infinite lasso shape word of the form x y for finite words x and y samples only a constant number of letters in x and y returns yes if w l a and returns no with probability 2 3 if w is e far from l a we also discuss the applicability of property testing to formal verification where regular languages are used for the specification of the behavior of nonterminating reactive systems and computations correspond to lasso shape words

propositional belief base merging or how to merge beliefs goals coming from several sources and some links with social choice theory abstract we give in this paper new results on merging operators those operators aim to define the goals or beliefs of an agents group after the individuals goals beliefs using the logical framework of konieczny and pino perez proceedings of the fifth european conference on symbolic and quantitative approaches to reasoning with uncertainty ecsqaru 99 lecture notes in artificial intelligence 1638 1999 pp 233 244 we study the relationships between two important sub families of merging operators majority operators and arbitration operators an open question was to know if those two families were disjoint or not we show that there are operators that belong simultaneously to the two families furthermore the new family introduced allows the user to choose the consensual level he wants for his majority operator we show at the end of this work some relationships between logical belief merging operators and social choice rules

the complexity of propositional linear temporal logics the complexity of satisfiability and determination of truth in a particular finite structure are considered for different propositional linear temporal logics it is shown that these problems are np complete for the logic with f and are pspace complete for the logics with f x with u with u s x operators and for the extended logic with regular operators given by wolper

efficient model checking for ltl with partial order snapshots certain behavioral properties of distributed systems are difficult to express in interleaving semantics whereas they are naturally expressed in terms of partial orders of events or equivalently mazurkiewicz traces two examples of such properties are serializability of a database and global snapshots of concurrent systems recently a modest extension for ltl by an operator that expresses snapshots has been proposed it combines the ease of linear interleaving specification with this useful partial order concept the new construct allows one to assert that a global snapshot appeared in the past perhaps not in the observed execution sequence but possibly in an equivalent one originally a model checking algorithm for this logic that is exponential space in the size of the system was suggested in this paper we provide a model checking algorithm that is in polynomial space in the size of the system our construction can also serve as an efficient polynomial algorithm for detecting conjunctive properties i e conjunction of local process properties in a concurrent history of execution

multivariate autoregressive techniques for constructing confidence regions on the mean vector we develop a method for constructing confidence regions on the mean vectors of multivariate processes that is based on a vector autoregressive var representation of the data generating process a confidence region construction algorithm for a general autoregressive model is given we establish the asymptotic validity of the confidence region estimator that is the exact achievement of nominal coverage probability as the sample size tends to infinity when the output process is a stationary vector autoregressive process of known finite order with respect to confidence region volume coverage probability and execution time we carry out an experimental performance comparison of var versus the methods of bonferroni batch means bbm multivariate batch means mbm and multivariate spectral analysis spa the experimental results indicate that i var delivered confidence regions with the smallest volume ii bbm delivered confidence regions with the largest volume the highest coverage and the smallest execution time iii in small samples all of the methods might yield confidence region estimators whose coverage differs significantly from the nominal level and iv in large samples for which the sample autocorrelation function indicates a vector autoregressive dependence structure var is a viable technique for simulation output analysis

alternating time temporal logics with linear past abstract we investigate the succinctness gap between two known equally expressive and different linear past extensions of standard atl we establish by formal non trivial arguments that the memoryful linear past extension the history leading to the current state is taken into account can be exponentially more succinct than the standard local linear past extension the history leading to the current state is forgotten as a second contribution we consider the atl like fragment denoted atl l p of the known memoryful linear past extension of atl we show that atl l p is strictly more expressive than atl and interestingly it can be exponentially more succinct than the more expressive logic atl moreover we prove that both satisfiability and model checking for the logic atl l p are exptime complete

the kl one family abstract the knowledge representation system kl one has been one of the most influential and imitated knowledge representation systems in the artificial intelligence community begun at bolt beranek and newman in 1978 kl one pioneered the development of taxonomic representations that can automatically classify and assimilate new concepts based on a criterion of terminological subsumption this theme generated considerab interest in both the formal community and a large community of potential users the kl one community has since expanded to include many systems at many institutions and in many different countries this paper introduces the kl one family and discusses some of the main themes explored by kl one and its successors we give an overview of current research describe some of the systems that have been developed and outline some future research directions

two theses of knowledge representation language restrictions taxonomic classification and the utility of representation services abstract levesque and brachman argue that in order to provide timely and correct responses in the most critical applications general purpose knowledge representation systems should restrict their languages by omitting constructs which require nonpolynomial worst case response times for sound and complete classification they also separate terminological and assertional knowledge and restrict classification to purely terminological information we demonstrate that restricting the terminological language and classifier in these ways limits these general purpose facilities so severely that they are no longer generally applicable we argue that logical soundness completeness and worst case complexity are inadequate measures for evaluating the utility of representation services and that this evaluation should employ the broader notions of utility and rationality found in decision theory we suggest that general purpose representation services should provide fully expressive languages classification over relevant contingent information approximate forms of classification involving defaults and rational management of inference tools

verification of gap order constraint abstractions of counter systems we investigate verification problems for gap order constraint systems gcs an infinitely branching abstract model of counter machines in which constraints over z between the variables of the source state and the target state of a transition are gap order constraints gc 32 gcs extend monotonicity constraint systems 7 integral relation automata 16 and constraint automata in 19 first we address termination and fairness analysis of gcs since gcs are infinitely branching termination does not imply strong termination i e the existence of an upper bound on the lengths of the runs from a given state we show that the termination problem the strong termination problem and the fairness problem for gcs the latter consisting in checking the existence of infinite runs in gcs satisfying acceptance conditions a la buchi are decidable and pspace complete moreover for each control location of the given gcs one can build a gc representation of the set of counter variable valuations from which termination resp strong termination resp fairness does not hold resp does not hold resp does hold next we consider a constrained branching time logic gcctl obtained by enriching ctl with gc thus enabling expressive properties and subsuming the setting of 16 we establish that while model checking gcs against the universal fragment of gcctl is undecidable model checking against the existential fragment and satisfiability of both the universal and existential fragments are instead decidable and pspace complete note that the two fragments are not dual since gc are not closed under negation moreover our results imply pspace completeness of known verification problems that were shown to be decidable in 16 with no elementary upper bounds

reasoning about infinite computations we investigate extensions of temporal logic by connectives defined by finite automata on infinite words we consider three different logics corresponding to three different types of acceptance conditions finite looping and repeating for the automata it turns out however that these logics all have the same expressive power and that their decision problems are all pspace complete we also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem