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A Coinductive Approach to Proving Reachability Properties in Logically Constrained Term Rewriting Systems [chapter]

Ştefan Ciobâcă, Dorel Lucanu
2018 Lecture Notes in Computer Science  
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo  ...  A key feature of the calculus is a circularity proof rule, which allows to obtain finite representations of the infinite coinductive proofs.  ...  For example, circular proof systems have been proposed for first-order logic with inductive predicates in [6] and for separation logic in [5] .  ... 
doi:10.1007/978-3-319-94205-6_20 fatcat:saprufevkzh65bfvu2hbclvbge

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  ...  On the other end, as a kind of minimal logic in this context, we consider FO(R) ("first-order logic with reachability"), the extension of first-order logic by a relation symbol for E * .  ... 
doi:10.1007/11562948_3 fatcat:z6i5hzxbvndrvj3rq52gqym5ju

Verification of Infinite State Systems [chapter]

Ahmed Bouajjani
2003 Lecture Notes in Computer Science  
During the two last decades, significant achievements have been obtained in the case of finite-state systems (systems with finitely many states).  ...  In the last two years the specification and verification of infinite-state systems have attracted the attention of more and more researchers belonging to a very broad range of research communities.  ...  In order to solve, even partially, this problem, one needs a representation system for potentially infinite sets of values, as well as a computation method for generating infinite sets of reachable states  ... 
doi:10.1007/978-3-540-45220-1_7 fatcat:4j5lzdbfc5hd7ptdo4tpwvmd2m

The Reachability Problem over Infinite Graphs [chapter]

Wolfgang Thomas
2009 Lecture Notes in Computer Science  
We survey classical and selected recent work on the reachability problem over finitely presented infinite graphs.  ...  The problem has a history of 100 years, and it is central for automatic verification of infinitestate systems. Our focus is on graphs that are presented in terms of word or tree rewriting systems.  ...  The first-order theory of an automatic graph is decidable, but -as seen above -an extension of first-order logic by the reachability relation leads to an undecidable theory.  ... 
doi:10.1007/978-3-642-03351-3_2 fatcat:ocehdjg765ejvbzjlb3qshwxve

Page 7838 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
To specify and study w-languages, various formalisms are used, such as logical calculi (first- and second-order monadic logics, temporal logics, y-calculi, etc.), algebraic systems (the algebra of regular  ...  A standard problem for infinite state systems is how to explore all states in a finite amount of time.  ... 

A Coinductive Approach to Proving Reachability Properties in Logically Constrained Term Rewriting Systems [article]

Ştefan Ciobâcă, Dorel Lucanu
2018 arXiv   pre-print
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo  ...  A key feature of the calculus is a circularity proof rule, which allows to obtain finite representations of the infinite coinductive proofs.  ...  We thank the anonymous reviewers for their valuable suggestions.  ... 
arXiv:1804.08308v1 fatcat:r6yoqb2oh5fqni7fkngd67wlru

Finite Model Finding for Parameterized Verification [article]

Alexei Lisitsa
2010 arXiv   pre-print
verification of large classes of infinite state and parameterized systems.  ...  The approach is based on modeling the reachability between (parameterized) states as deducibility between suitable encodings of states by formulas of first-order predicate logic.  ...  The encoding of infinite state systems in first-order predicate logic is used in the MCMT deductive symbolic model checker [9, 10] .  ... 
arXiv:1011.0447v2 fatcat:eeiehou3hnhjpcpnxzvskbnz64

Contents and abstracts of the electronic notes in Theoretical Computer Science Vol. 5

1998 Theoretical Computer Science  
and (2) given an infinite-state system and a property expressed in a certain temporal logic, does the system satisfy the property?  ...  Showing strong early bisimulation between finite symbolic transition graphs extended with assignments is reduced to solving sets of equations involving first-order state formulas.  ...  Kapron A modal p-calculus and a pvoof system fov value-passing pvocesses http://www.elsevier.nl/locate/entcs/volue5.html A first-order modal p-calculus is introduced as a convenient logic for reasoning  ... 
doi:10.1016/s0304-3975(97)00248-x fatcat:sdn5br4hkvhjnowkexgso4rute

Matching mu-Logic: Foundation of K Framework (Invited Paper)

Xiaohong Chen, Grigore Rosu, Michael Wagner
2019 Conference on Algebra and Coalgebra in Computer Science  
, and reachability logic.  ...  In this extended abstract, we present matching µ-logic as the foundation of K and discuss some of its applications in defining constructors, transition systems, modal µ-logic and temporal logic variants  ...  To overcome this limitation, we recently proposed matching µ-logic [2] , which is a powerful logic that subsumes not only matching logic and reachability logic, but also first-order logic with least fixpoints  ... 
doi:10.4230/lipics.calco.2019.1 dblp:conf/calco/0002R19 fatcat:vkyvq4ybm5cr5c3qgnmah2z2jy

Temporal Logics over Transitive States [chapter]

Boris Konev, Frank Wolter, Michael Zakharyaschev
2005 Lecture Notes in Computer Science  
The proofs are based on Kruskal's tree theorem and reductions of reachability problems for lossy channel systems.  ...  Finally, we show that temporal logics over infinite expanding domains as above are undecidable even for the language with the sole temporal operator 'eventually.'  ...  Schnoebelen, and the members of the London Logic Forum for stimulating discussions, comments and suggestions. The work on this paper was partially supported by U.K. EPSRC grants no.  ... 
doi:10.1007/11532231_14 fatcat:bjvs534zkzc2ff2nyu2zj4k5cq

Towards a Model-Checker for Counter Systems [chapter]

S. Demri, A. Finkel, V. Goranko, G. van Drimmelen
2006 Lecture Notes in Computer Science  
This paper deals with model-checking of fragments and extensions of CTL* on infinite-state Presburger counter systems, where the states are vectors of integers and the transitions are determined by means  ...  Finally, we design a complete semi-algorithm to verify first-order LTL properties over trace-flattable counter systems, extending the previous underlying FAST semi-algorithm to verify reachability questions  ...  The single most important property of practical interest in infinite-state transition systems is state reachability which is often undecidable in structures with otherwise decidable first-order theories  ... 
doi:10.1007/11901914_36 fatcat:v2iri7t2cfcv3phe6unqer6sxq

Memory-efficient algorithms for the verification of temporal properties

C. Courcoubetis, M. Vardi, P. Wolper, M. Yannakakis
1992 Formal methods in system design  
This paper addresses the problem of designing memory-efficient algorithms for the verification of temporal properties of finite-state programs.  ...  By allowing the algorithms to err with some probability, we can implement them with a randomly accessed memory of size O(n) bits, where n is the number of states of the graph, instead of O(n log n) bits  ...  Given a program P described as the concurrent execution of finite-state transition systems P i and a temporal logic formula f , check that all infinite computations of P satisfy f .  ... 
doi:10.1007/bf00121128 fatcat:jwvsskomonasrlaffnwrumjgtm

Checking reachability using matching logic

Grigore Rosu, Andrei Stefanescu
2012 Proceedings of the ACM international conference on Object oriented programming systems languages and applications - OOPSLA '12  
The proof system is proved partially correct and relatively complete (with respect to the programming language configuration model).  ...  The underlying proof system is languageindependent and consists of eight proof rules.  ...  Acknowledgements: We thank the members of the K team (http://k-framework.org) and the anonymous reviewers for their valuable comments on a previous version of this paper.  ... 
doi:10.1145/2384616.2384656 dblp:conf/oopsla/RosuS12 fatcat:jsggbf2tfzh7hepfoagrtd4bge

Memory-Efficient Algorithms for the Verification of Temporal Properties [chapter]

C. Courcoubetis, M. Vardi, P. Wolper, M. Yannakakis
1992 Computer-Aided Verification  
This paper addresses the problem of designing memory-efficient algorithms for the verification of temporal properties of finite-state programs.  ...  By allowing the algorithms to err with some probability, we can implement them with a randomly accessed memory of size O(n) bits, where n is the number of states of the graph, instead of O(n log n) bits  ...  Given a program P described as the concurrent execution of finite-state transition systems P i and a temporal logic formula f , check that all infinite computations of P satisfy f .  ... 
doi:10.1007/978-1-4615-3556-0_5 fatcat:prb4ib6njfc37hjcyfytuanjoi

A Three-Value Abstraction Technique for the Verification of Epistemic Properties in Multi-agent Systems [chapter]

Francesco Belardinelli, Alessio Lomuscio
2016 Lecture Notes in Computer Science  
First we introduce a three-value interpretation of epistemic logic, based on a notion of order defined on the information content of the local states of each agent.  ...  Then, we use the three-value semantics to introduce an abstraction technique to verify epistemic properties of agents in infinite-state multi-agent systems.  ...  We first consider an example of an interpreted system with a partial order defined on each agent's local states.  ... 
doi:10.1007/978-3-319-48758-8_8 fatcat:sitnjdw5sfeybobrzytw3xb5i4
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