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

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

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

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

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

new algorithm for observer error linearization with a diffeomorphism on the outputs in this paper we give the necessary and sufficient conditions that guarantee the existence of a diffeomorphism which allows one to transform a multi output nonlinear dynamical system into a normal observable canonical form in particular we propose an algorithm that permits one to derive such diffeomorphism the main feature of the canonical form is that it is obtained by allowing a diffeomorphism on the outputs and it also allows one to design an observer with linear error dynamics we first consider multi output nonlinear dynamical system without inputs we then extend the results obtained to multi output nonlinear dynamical system with inputs

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

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

time scaling for observer design with linearizable error dynamics in this paper we consider the problem of observer design for dynamical systems with scalar output by linearization of the error dynamics via coordinate change output injection and time scaling we present necessary and sufficient conditions which guarantee the existence of a coordinate change and output dependent time scaling such that in the new coordinates and with respect to the new time the system has linear error dynamics

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

nonlinear observer design for a general class of discrete time nonlinear systems with real parametric uncertainty this paper is a geometric study of the local observer design for a general class of discrete time nonlinear systems with real parametric uncertainty explicitly we study the observer design problem for a general class of discrete time nonlinear systems with real parametric uncertainty and with an input generator exosystem in this paper we show that for the classical case when the state equilibrium does not change with the parametric uncertainty and when the plant output is purely a function of the state there is no local asymptotic observer for the plant next we show that in sharp contrast to this case for the general case of problems where we allow the state equilibrium to change with the parametric uncertainty there typically exist local exponential observers even when the plant output is purely a function of the state we also present a characterization and construction procedure for local exponential observers for the general class of discrete time nonlinear systems with real parametric uncertainty under some stability assumptions we also show that for the general class of discrete time nonlinear systems considered under some stability assumptions the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs finally we generalize our results to a general class of discrete time nonlinear systems with input generator and with exogenous disturbance

a block triangular nonlinear observer normal form abstract the nonlinear observer normal form is generalized to a block triangular observer normal form which can be interpreted as a series connection of subsystems in observer form based on this new form exponential observers can be designed using methods from the linear case necessary and sufficient conditions for the existence of state transformations into this normal form are given

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

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

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

dynamic observer error linearization in this paper a new framework of observer error linearization problem is proposed the main idea of our approach is twofold the one is to introduce an auxiliary dynamics whose input is the system output and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics it is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output it is also shown that whenever an n dimensional system is immersible into an n d dimensional linear system up to an output injection then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics moreover we show that the converse is not true by providing a counterexample which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method

a conservative level set method for two phase flow ii in this paper we continue to develop and study the conservative level set method for incompressible two phase flow with surface tension introduced in j comput phys 210 2005 225 246 we formulate a modification of the reinitialization and present a theoretical study of what kind of conservation we can expect of the method a finite element discretization is presented as well as an adaptive mesh control procedure numerical experiments relevant for problems in petroleum engineering and material science are presented for these problems the surface tension is strong and conservation of mass is important problems in both two and three dimensions with uniform as well as non uniform grids are studied from these calculations convergence and conservation is studied good conservation and convergence are observed

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

nonlinear estimation in a class of gene transcription process in this work the goodwin model applied to gene transcription is employed as a benchmark system for estimation purposes considering two dynamic behaviors monotone decreasing and sustained oscillations each one under a specific parameter s set the preceding observability analysis of the goodwin model was done via linear observability and the differential algebraic framework where is proved that the system is fully observable from mrna concentration measurements therefore a class of nonlinear observer which considers a class of sigmoid and linear functions of the output feedback considering model uncertainties is proposed and a sketch of proof of the observer s convergence is provided under the background of the lyapunov theory in order to demonstrate asymptotic convergence numerical experiments are carrying out in order to show the performance of the proposed methodology which is compared with a standard luenberger proportional observer and a proportional sliding mode observer psmo

reduced order dynamic observer error linearisation a natural extension of observer error linearisation this paper introduces the concept of reduced order dynamic observer error linearisation rdoel for multi output systems which is the problem of transforming a nonlinear system into a nonlinear observer canonical form with the aid of auxiliary dynamics the proposed rdoel framework is not only a modified version of dynamic observer error linearisation doel but also a natural extension of observer error linearisation oel we provide three necessary conditions for the rdoel problem and then derive a necessary and sufficient condition described in terms of lie algebras of vector fields furthermore from the result we also give a geometric necessary and sufficient condition for the oel problem which has not yet been completely established in the case where a diffeomorphism on the output of general form is considered

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

an efficient method for observer design with approximately linear error dynamics exact error linearization is a well known full order observer design method which yields linear time invariant stable error dynamics in normal form coordinates the difficult procedure associated with exact error linearization has led to the simpler extended luenberger observer design however extended luenberger observers can only guarantee a first order approximation to the exact error linearization design this paper provides an explicit formula involving only derivative lie derivative and bracket and matrix inversion operations for computing an nth order approximation of the exact error linearization observer hence the proposed method is a computational simple tool for designing observers for systems admitting exact error linearization observers two examples demonstrate the application of the method

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

constructive algorithm for system immersion into non linear observer form there exists a class of non linear systems which cannot be transformed into a non linear observer form an observable linear system up to output injection via diffeomorphism but can be immersed into a higher dimensional non linear observer form this class of systems can be characterized by a differential equation called characteristic equation if the system is an n dimensional system and it is immersible into n m dimensional observer form the characteristic equation involves n m 1 unknowns where n m unknowns are for the state immersion and one for the output transformation in general one should solve these unknowns simultaneously which makes the characterization difficult after investigating the algebraic structure of the characteristic equation we present an algorithm to check the immersibility under a constant rank assumption using the algorithm one can check the immersibility iteratively since only one unknown is involved at each step of the algorithm

nonlinear observer design for a general class of nonlinear systems with real parametric uncertainty this paper is a geometric study of the local observer design for a general class of nonlinear systems with real parametric uncertainty explicitly we study the observer design problem for a general class of nonlinear systems with real parametric uncertainty and with an input generator exosystem in this paper we show that for the classical case when the state equilibrium does not change with the parametric uncertainty and when the plant output is purely a function of the state there is no local asymptotic observer for the plant next we show that in sharp contrast to this case for the general case of problems where we allow the state equilibrium to change with the parametric uncertainty there typically exist local exponential observers even when the plant output is purely a function of the state we also present a characterization and construction procedure for local exponential observers for the general class of nonlinear systems with real parametric uncertainty under some stability assumptions we also show that for the general class of nonlinear systems considered under some stability assumptions the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs finally we generalize our results to a general class of nonlinear systems with input generator and with exogenous disturbance

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

on output transformations for state linearization up to output injection steering a nonlinear system into a so called state affine one up to output injection by change of coordinates is of much interest for observer design this interest is preserved by also considering changes of output the purpose of the paper is then to provide computable conditions for existence of output transformations making a system which is not transformable into a state affine one up to output injection by only a change of coordinates to become so after a change of output such a characterization enlarges the class of systems for which an observer is available

new algebraic geometric conditions for the linearization by input output injection the goal of this paper is twofold it unifies and generalizes existing results on input output injection linearization of nonlinear systems the problem is solved as a realization problem since it is based on the analysis of the structure of the input output differential equation the necessary and sufficient conditions are derived from a simplified and constructive procedure for clarity the paper is limited to the case of single output systems exterior differential systems are extensively used throughout the paper giving constructive conditions

a new reduced order observer normal form for nonlinear discrete time systems this paper presents a new observability normal form for discrete time nonlinear systems this form enables us to design a reduced order observer necessary and sufficient geometrical conditions for the existence of a coordinate change to transform a discrete time nonlinear system into such normal form are given an illustrative example is given to show the effectiveness of our approach

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

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

on constructing nonlinear observers two algorithmic approaches to constructing nonlinear observers currently exist here one of these is improved by finding an explicit solution to the partial differential equations describing the change of state coordinates thereby avoiding expensive bracket computations this simplifies the algorithm and has implications for system identification

linearization by generalized input output injection abstract the problem under interest is the linearization of nonlinear mimo systems by generalized input output injection in order to design observers with linear error dynamics the method is based on the study of the structure of the input output differential equations thus the problem is solved as a realization problem in this note one considers the linearization under two kinds of inout output injection in the first case the transformation depends on the output and time derivatives of the input whereas in the second case derivatives of both the input and the output are considered necessary and sufficient conditions are obtained which generalize the ones on standard input output injection linearization

observer design based on immersion technics and canonical form abstract a crucial problem in immersion based observer design is the case where the dimension of the immersed system is greater than that of the original system and the analytical expression of the inverse of the immersion is unknown in this paper we have proposed a method for constructing observers for such autonomous nonlinear systems

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

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

extended output depending normal form this paper concerns the design of a nonlinear observer through a transformation of a nonlinear system into an observer form that supports a high gain observer sufficient geometrical condition is deduced to guarantee the existence of change of coordinates allowing the transformation of a nonlinear system into the proposed normal form the result is highlighted by studying the susceptible exposed infected and recovered seir model

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

partial observer normal form for nonlinear system in this paper we investigate the estimation problem for a class of partially observable nonlinear systems for the proposed partial observer normal form ponf necessary and sufficient conditions are deduced to guarantee the existence of a change of coordinates which can transform the studied system into the proposed ponf examples are provided to illustrate the effectiveness of the proposed results

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

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

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

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 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

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

a lattice boltzmann model for multiphase flows with large density ratio a lattice boltzmann model for simulating multiphase flows with large density ratios is described in this paper the method is easily implemented it does not require solving the poisson equation and does not involve the complex treatments of derivative terms the interface capturing equation is recovered without any additional terms as compared to other methods m r swift w r osborn j m yeomans lattice boltzmann simulation of liquid gas and binary fluid systems phys rev e 54 1996 5041 5052 t inamuro t ogata s tajima n konishi a lattice boltzmann method for incompressible two phase flows with large density differences j comput phys 198 2004 628 644 t lee c l lin a stable discretization of the lattice boltzmann equation for simulation of incompressible two phase flows at high density ratio j comput phys 206 2005 16 47 besides it requires less discrete velocities as a result its efficiency could be greatly improved especially in 3d applications it is validated by several cases a bubble in a stationary flow and the capillary wave the numerical surface tension obtained from the laplace law and the interface profile agrees very well with the respective analytical solution the method is further verified by its application to capillary wave and the bubble rising under buoyancy with comparison to other methods all the numerical experiments show that the present approach can be used to model multiphase flows with large density ratios

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

on the transformation of nonlinear dynamical systems into the extended nonlinear observable canonical form this article deals with the transformation of a class of nonlinear systems into an extended nonlinear observable canonical form enocf by dynamic extension the dynamic extension is obtained by adding auxiliary dynamics and virtual outputs to the original system thus giving rise to a higher dimensional system in an extended state space sufficient geometrical conditions to guarantee the existence of a local diffeomorphism which allow the transformation of the extended system into the enocf are given in particular an algorithm that permits us to compute such a diffeomorphism is derived

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

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