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From Well Structured Transition Systems to Program Verification

Alain Finkel
2020 Electronic Proceedings in Theoretical Computer Science  
We describe the use of the theory of WSTS for verifying programs.  ...  We have also to translate the property φ on P into a state-property φ S in (S, →) (sometimes a formula in a logic) that would be decidable for WSTS. 2.  ...  The ordering which is not well on the considered set of states could be well on the subset of reachable states.  ... 
doi:10.4204/eptcs.320.3 fatcat:ex6susvyvvajjpgy7vqstaoeaq

Page 3554 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
The finite power problem is the problem of deciding whether a recognizable language has the FPP property; a language T has the FPP property if L* = L°U---UL", for some integer n.  ...  The proof is based on the analysis of some global topological properties of the configuration graph of a self-stabilizing Turing machine.  ... 

Regular Language Representations in the Constructive Type Theory of Coq

Christian Doczkal, Gert Smolka
2018 Journal of automated reasoning  
We give translations between all representations, show decidability results, and provide operations for various closure properties.  ...  Our results include a constructive decidability proof for the logic WS1S, a constructive refinement of the Myhill-Nerode characterization of regularity, and translations from twoway automata to one-way  ...  Acknowledgements We thank Jan-Oliver Kaiser, who was involved in our previous work on one-way automata and also in some of the early experiments with two-way automata.  ... 
doi:10.1007/s10817-018-9460-x fatcat:43r6bknxpzhhrhj5tdhn2qnb6e

Finite-Trace Linear Temporal Logic: Coinductive Completeness [chapter]

Grigore Roşu
2016 Lecture Notes in Computer Science  
The axioms and proof rules are natural and expected, except for one rule of coinductive nature, reminiscent of the Gödel-Löb axiom.  ...  The completeness of LTL with only infinite or with both infinite and finite traces has been extensively studied, but similar direct results for LTL with only finite traces are missing.  ...  When giving LTL a finite-trace semantics, one has to decide upon the semantics of the "next" operator on one-state traces, that is, when there is no next state.  ... 
doi:10.1007/978-3-319-46982-9_21 fatcat:zrpfkrm6xne33g6sdyja3c4pea

Page 3879 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
Lisovik (UKR-KIEV-A; Kiev) 98f:68192 68Q70 04472 20N25 Das, Pratyayananda (6-BURD; Burdwan) On some properties of fuzzy semiautomaton over a finite group. (English summary) Inform.  ...  Since often we want to specify that all the computations of the program satisfy some property, the interest in derived languages is clear.  ... 

Page 2148 of Mathematical Reviews Vol. , Issue 86e [page]

1986 Mathematical Reviews  
“We investigate some properties of AMHFAs with only univer- sal states (UMHFAs). Section 2 gives terminology and notation necessary for this paper.  ...  Author summary: “We propose a translation method of finite terms of CCS into formulas of a modal language representing their class of observational congruence.  ... 

Translation-like Actions and Aperiodic Subshifts on Groups [article]

Emmanuel Jeandel
2015 arXiv   pre-print
"H is a subgroup of G"by "H acts translation-like on G", provided H is finitely presented.In particular:* If G_1 and G_2 are f.g. infinite groups, then G_1 × G_2 has a weakly aperiodic SFT (and actually  ...  admits a f.g. subgroup H with a weaklyaperiodic SFT (resp. an undecidable domino problem), then Gitself has a weakly aperiodic SFT (resp. an undecidable domino problem).We prove that we can replace the property  ...  If every subshift of finite type is periodic, this implies some properties on the lattice of subgroups of finite index.  ... 
arXiv:1508.06419v1 fatcat:dnrdibpfuvbkfgcml2e7kfoaee

Page 4009 of Mathematical Reviews Vol. , Issue 87h [page]

1987 Mathematical Reviews  
Properties of these sub- stitution operators are established and some deductive criteria for them are proved, somewhat analogous to the substitution criteria and deductive criteria in Bourbaki’s Theory  ...  Although not needed for the decidability proof, a converse theorem is also shown stating that any pda has a context- free state graph.  ... 

A Constructive Theory of Regular Languages in Coq [chapter]

Christian Doczkal, Jan-Oliver Kaiser, Gert Smolka
2013 Lecture Notes in Computer Science  
We construct computable functions translating between these representations and show that equivalence of representations is decidable.  ...  We also establish the usual closure properties, give a minimization algorithm for DFAs, and prove that minimal DFAs are unique up to state renaming.  ...  We thank the anonymous reviewers of the preliminary versions of this paper for their helpful comments.  ... 
doi:10.1007/978-3-319-03545-1_6 fatcat:n6zqnsmccna3vbrnwjfv52fcxa

Decidability of finite probabilistic propositional dynamic logics

M. Tiomkin, J.A. Makowsky
1991 Information and Computation  
Some of these logics have the finite model property, and therefore. if they are undecidable, they are exactly f7:. We show that allowing nesting and probabilistic choice often leads to undecidability.  ...  We investigate the (un)decidability of these logics and give a complete picture of decidability and undecidability.  ...  Hare1 for helpful comments on the paper. Special thanks go to two anonymous referees for carefully reading the first versions and making valuable criticism which improved the paper essentially.  ... 
doi:10.1016/0890-5401(91)90037-3 fatcat:fiaicoh32zadrkzff6tnokizfm

An Automata-Theoretic Approach to Reasoning about Parameterized Systems and Specifications [chapter]

Orna Grumberg, Orna Kupferman, Sarai Sheinvald
2013 Lecture Notes in Computer Science  
We demonstrate the usefulness of the approach by pushing forward the known border of decidability for the modelchecking problem in this setting.  ...  We show that GRAs can capture both VLTL -a logic that extends LTL with variables over infinite domains, and abstract systems -finite state systems whose atomic propositions are parameterized by variable  ...  , -Q is a finite set of states, -q 0 is the initial state, -F ⊆ Q is a set of accepting states, and We describe a run of a GRA on an input word w.  ... 
doi:10.1007/978-3-319-02444-8_28 fatcat:2ge5kkx4kbfsxls442ekuuanqq

Page 614 of Mathematical Reviews Vol. 57, Issue 2 [page]

1979 Mathematical Reviews  
The theory is not star- tling, but provides some additional insight into translations and parsing.  ...  The author concludes that the methods discussed are sufficiently powerful to analyze some of the information-theoretic properties of real programming languages.  ... 

Regularity and Related Problems for Deterministic Pushdown Automata

Leslie G. Valiant
1975 Journal of the ACM  
It ~S shown that to decide whether the language accepted by an arbitrary deterministic pushdown automaton is LL (k), or whether ~t m accepted by some one-counter or finite-turn pushdown machine, must be  ...  , program schema CR CATEGORIES. 5 22, 5.24 has shown that the function defined as the size of the largest reduced finite automaton  ...  The decidability of each of the containment problems (dpda : V), where V is one of the subclasses so far mentioned, is currently open, except for the case of finite-state automata, for which a decision  ... 
doi:10.1145/321864.321865 fatcat:5zazbxhmnrgxnbgbi6gpf5vaga

Some Perspectives of Infinite-State Verification [chapter]

Wolfgang Thomas
2005 Lecture Notes in Computer Science  
We report on recent progress in the study of infinite transition systems for which interesting properties (like reachability of designated states) can be checked algorithmically.  ...  Two methods for the generation of such models are discussed: the construction from simpler models via operations like unfolding and synchronized product, and the internal representation of state spaces  ...  It can be generalized in several ways while keeping (at least some of) the mentioned decidability properties.  ... 
doi:10.1007/11562948_3 fatcat:z6i5hzxbvndrvj3rq52gqym5ju

Towards Model-Checking Programs with Lists [chapter]

Alain Finkel, Étienne Lozes, Arnaud Sangnier
2009 Lecture Notes in Computer Science  
We first explain how a translation of programs into counter systems can be used to check safety problems and temporal properties.  ...  We then study the decidability of these two problems considering some restricted classes of programs, namely flat programs without destructive update.  ...  Note that since a counter system has a finite number of control states and of transitions, one can decide whether a counter system is flat or not.  ... 
doi:10.1007/978-3-642-03092-5_6 fatcat:jso5f5fmxzclplmx3tmzsyoskm
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