countable nondeterminism and random assignment four semantics for a small programming language involving unbounded but countable nondeterminism are provided these comprise an operational semantics two state transformation semantics based on the egli milner and smyth orders respectively and a weakest precondition semantics their equivalence is proved a hoare like proof system for total correctness is also introduced and its soundness and completeness in an appropriate sense are shown finally the recursion theoretic complexity of the notions introduced is studied admission of countable nondeterminism results in a lack of continuity of various semantic functions and this is shown to be necessary for any semantics satisfying appropriate conditions in proofs of total correctness one resorts to the use of countable ordinals and it is shown that all recursive ordinals are needed

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

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

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

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

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

the m calculus as an assertion language for fairness arguments abstract various principles of proof have been proposed to reason about fairness this paper addresses for the first time the question in what formalism such fairness arguments can be couched to wit we prove that park s monotone first order calculus augmented with constants for all recursive ordinals can serve as an assertion language for proving fair termination of do loops in particular the weakest precondition for fair termination of a loop w r t some postcondition is definable in it the relevance of this result to proving eventualities in the temporal logic formalism of manna and pnuelis in foundations of computer science iv part 2 math centre tracts vol 159 math centrum amsterdam 1983 is discussed

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

spatiotemporal dynamics of continuum neural fields we survey recent analytical approaches to studying the spatiotemporal dynamics of continuum neural fields neural fields model the large scale dynamics of spatially structured biological neural networks in terms of nonlinear integrodifferential equations whose associated integral kernels represent the spatial distribution of neuronal synaptic connections they provide an important example of spatially extended excitable systems with nonlocal interactions and exhibit a wide range of spatially coherent dynamics including traveling waves oscillations and turing like patterns

existence and uniqueness of travelling waves for a neural network a one dimensional scalar neural network with two stable steady states is analysed it is shown that there exists a unique monotone travelling wave front which joins the two stable states some additional properties of the wave such as the direction of its velocity are discussed

traveling fronts and wave propagation failure in an inhomogeneous neural network we use averaging and homogenization theory to study the propagation of traveling wavefronts in an inhomogeneous excitable neural medium motivated by the functional architecture of primary visual cortex we model the inhomogeneity as a periodic modulation in the long range neuronal connections we derive an expression for the effective wavespeed and show that propagation failure can occur if the speed is too slow or the degree of inhomogeneity is too large we find that there are major qualitative differences in the wavespeed for different choices of the homogenized weight distribution

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 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

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

likelihood based modelling of age related normal ranges for ordinal measurements changes in visual acuity through early childhood this paper investigates the construction of age related standards for ordinal outcome data asymmetric logistic models are used to describe the age related changes in the cumulative probabilities for each ordinal level maximum likelihood estimation of model parameters allows the use of likelihood ratio tests to ascertain the appropriate model complexity in contrast to methodologies for constructing age related standards where the outcome is continuous we show how the methodology leads directly to centile estimation for individuals the method is illustrated using visual acuity measurements collected from 2968 children between 2 and 9 years of age made on a 30 point ordinal scale we show how in this instance smoothing of parameters across ordinal categories leads to reduced validity of the centiles justifying the need for specialized methodology for non continuous outcomes

stimulus locked traveling waves and breathers in an excitatory neural network we analyze the existence and stability of stimulus locked traveling waves in a one dimensional synaptically coupled excitatory neural network the network is modeled in terms of a nonlocal integro differential equation in which the integral kernel represents the spatial distribution of synaptic weights and the output firing rate of a neuron is taken to be a heaviside function of activity given an inhomogeneous moving input of amplitude i0 and velocity v we derive conditions for the existence of stimulus locked waves by working in the moving frame of the input we use this to construct existence tongues in v i0 parameter space whose tips at i0 0 correspond to the intrinsic waves of the homogeneous network we then determine the linear stability of stimulus locked waves within the tongues by constructing the associated evans function and numerically calculating its zeros as a function of network parameters we show that as the input amplitude is reduced a stimulus locked wave within the tongue of

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

goodness of fit statistics for age specific reference intervals the age specific reference interval is a commonly used screening tool in medicine it involves estimation of extreme quantile curves such as the 5th and 95th centiles of a reference distribution of clinically normal individuals it is crucial that models used to estimate such intervals fit the data extremely well however few procedures to assess goodness of fit have been proposed in the literature and even fewer have been evaluated systematically here we consider procedures based on the distribution of the z scores standardized residuals from a model and on pearson chi 2 statistics for observed and expected counts in groups defined by age and the estimated reference centile curves two of the procedures q and grid tests are mainly inferential whereas the third permutation bands and b tests is essentially graphical we obtain approximations to the null distributions of several relevant test statistics and examine their size and power for a range of models based on real data sets we recommend q tests in all situations where z scores are available since they are general simple to calculate and usually have the highest power among the three classes of test considered for the cases considered the grid tests are always inferior to the q and b tests

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

phase description of oscillatory convection with a spatially translational mode abstract we formulate a theory for the phase description of oscillatory convection in a cylindrical hele shaw cell that is laterally periodic this system possesses spatial translational symmetry in the lateral direction owing to the cylindrical shape as well as temporal translational symmetry oscillatory convection in this system is described by a limit torus solution that possesses two phase modes one is a spatial phase and the other is a temporal phase the spatial and temporal phases indicate the position and oscillation of the convection respectively the theory developed in this paper can be considered as a phase reduction method for limit torus solutions in infinite dimensional dynamical systems namely limit torus solutions to partial differential equations representing oscillatory convection with a spatially translational mode we derive the phase sensitivity functions for spatial and temporal phases these functions quantify the phase responses of the oscillatory convection to weak perturbations applied at each spatial point using the phase sensitivity functions we characterize the spatiotemporal phase responses of oscillatory convection to weak spatial stimuli and analyze the spatiotemporal phase synchronization between weakly coupled systems of oscillatory convection

age related standards for ordinal data modelling the changes in visual acuity from 2 to 9 years of age the visual acuities of 1140 children between the ages of 2 and 9 years were measured using the sonksen silver acuity system ssas from a distance of 3 metres ordered logistic regression was used to construct smoothly changing age related reference ranges for the proportions of children at different ages expected to have acuities in each of three ordinal categories exponential functions of age fitted the data better than polynomials the resulting reference ranges can be used to derive the ages at which a given percentage of children achieve each of the acuity cut offs however since it is unlikely that all children will be available for testing at the exact appropriate age two possible alternatives are introduced and discussed first a new ordinal category that would result in a chosen outcome at a pre selected age is calculated secondly because it may be more feasible to use the current ssas system whilst varying the distance of measurement age related standards showing the distances required to give constant pass rates with the usual letter sizes are also presented

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

wandering bumps in a stochastic neural field a variational approach abstract we develop a generalized variational method for analyzing wandering bumps in a stochastic neural field model defined on some domain u for concreteness we take u s 1 and consider a stochastic ring model first we decompose the stochastic neural field into a phase shifted deterministic bump solution and a small error term which is assumed to be valid up to some exponentially large stopping time an exact implicit stochastic differential equation sde for the phase of the bump is derived by minimizing the error term with respect to a weighted l 2 u norm the positive weight is chosen so that the error term consists of fast transverse fluctuations of the bump profile we then carry out a perturbation series expansion of the exact variational phase equation in powers of the noise strength to obtain an explicit nonlinear sde for the phase that decouples from the error term solving the corresponding steady state fokker planck equation up to o we determine a leading order expression for the long time distribution of the position of the bump finally we use the variational formulation to obtain rigorous exponential bounds on the error term demonstrating that with very high probability the system stays in a small neighborhood of the bump for times of order exp c 1

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

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

the link between integral equations and higher order odes we study a class of partial integro differential equations defined on a spatially extended domain that arise in the modeling of neuronal networks in previous studies the fourier transform was used to derive associated fourth order ordinary differential equations when the solution of the time independent integral equation is a homoclinic orbit this gives rise to the question of whether solutions of the ode whose fourier transform is not well defined are also solutions of the time independent integral equation we address this question and show that any solution of the ode that satisfies a fairly relaxed growth condition is also a solution of the integral equation applications to two specific examples are given

a proof rule for fair termination of guarded commands we present a proof rule for fairly terminating guarded commands based on a well foundedness argument the rule is applied to several examples and proved to be sound and semantically complete w r t an operational semantics of computation trees the rule is related to another rule suggested by lehmann pnueli and stavi in proc internat colloq automata lang and programming 81 acre july 1981 by showing that the semantic completeness of the lps rule follows from the completeness or ours

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

spatially structured activity in synaptically coupled neuronal networks i traveling fronts and pulses we consider traveling front and pulse solutions to a system of integro differential equations used to describe the activity of synaptically coupled neuronal networks in a single spatial dimension our first goal is to establish a series of direct links between the abstract nature of the equations and their interpretation in terms of experimental findings in the cortex and other brain regions this is accomplished first by presenting a biophysically motivated derivation of the system and then by establishing a framework for comparison between numerical and experimental measures of activity propagation speed our second goal is to establish the existence of traveling pulse solutions using more rigorous methods two techniques are presented the first a shooting argument reduces the problem from finding a specific solution to an integro differential equation system to finding any solution to an ode system the second a singular perturbation argument provides a construction of traveling pulse solutions un

stimulus driven traveling solutions in continuum neuronal models with a general smooth firing rate function we examine the existence of traveling wave solutions for a continuum neuronal network modeled by integro differential equations first we consider a scalar field model with a general smooth firing rate function and a spatiotemporally varying stimulus we prove that a traveling front solution that is locked to the stimulus exists for a certain interval of stimulus speeds next we include a slow adaptation equation and obtain a formula which involves a certain adjoint solution for the stimulus speeds that induce locked traveling pulse solutions further we use singular perturbation analysis to characterize an approximation to the adjoint solution that we compare to a numerically computed adjoint numerical simulations are used to illustrate the traveling fronts and pulses that we study and to make comparisons with our analytically computed bounds for stimulus locked wave behavior

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

traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators abstract motivated by earlier studies of artificial perceptions of light called phosphenes we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon we examine the discrete model problem in its co traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable and these waves are in turn connected to the standing waves analyzed in earlier work we also consider a two dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out depending on the phase value inside and the parameter regime finally we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes

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

phase equations for relaxation oscillators we use the malkin theorem to derive phase equations for networks of weakly connected relaxation oscillators we find an explicit formula for the connection functions when the oscillators have one dimensional slow variables the functions are discontinuous in the relaxation limit mu rightarrow 0 which provides a simple alternative illustration to the major conclusion of the fast threshold modulation ftm theory by somers and kopell biological cybernetics 68 1993 pp 393 407 that synchronization of relaxation oscillators has properties that are quite different from those of smooth nonrelaxation oscillators we use bonhoeffer van der pol relaxation oscillators to illustrate the theory numerically

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