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

2018
*
Lecture Notes in Computer Science
*

We introduce a sound and complete coinductive proof

doi:10.1007/978-3-319-94205-6_20
fatcat:saprufevkzh65bfvu2hbclvbge
*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] . ...##
###
Some Perspectives of Infinite-State Verification
[chapter]

2005
*
Lecture Notes in Computer Science
*

We report on recent progress in the study of

doi:10.1007/11562948_3
fatcat:z6i5hzxbvndrvj3rq52gqym5ju
*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 * . ...##
###
Verification of Infinite State Systems
[chapter]

2003
*
Lecture Notes in Computer Science
*

During the two last decades, significant achievements have been obtained in the case of finite-

doi:10.1007/978-3-540-45220-1_7
fatcat:4j5lzdbfc5hd7ptdo4tpwvmd2m
*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*...##
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The Reachability Problem over Infinite Graphs
[chapter]

2009
*
Lecture Notes in Computer Science
*

We survey classical and selected recent work on the

doi:10.1007/978-3-642-03351-3_2
fatcat:ocehdjg765ejvbzjlb3qshwxve
*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. ...##
###
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]

2018
*
arXiv
*
pre-print

We introduce a sound and complete coinductive proof

arXiv:1804.08308v1
fatcat:r6yoqb2oh5fqni7fkngd67wlru
*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. ...##
###
Finite Model Finding for Parameterized Verification
[article]

2010
*
arXiv
*
pre-print

verification of large classes of

arXiv:1011.0447v2
fatcat:eeiehou3hnhjpcpnxzvskbnz64
*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] . ...##
###
Contents and abstracts of the electronic notes in Theoretical Computer Science Vol. 5

1998
*
Theoretical Computer Science
*

and (2) given an

doi:10.1016/s0304-3975(97)00248-x
fatcat:sdn5br4hkvhjnowkexgso4rute
*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 ...##
###
Matching mu-Logic: Foundation of K Framework (Invited Paper)

2019
*
Conference on Algebra and Coalgebra in Computer Science
*

, and

doi:10.4230/lipics.calco.2019.1
dblp:conf/calco/0002R19
fatcat:vkyvq4ybm5cr5c3qgnmah2z2jy
*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 ...##
###
Temporal Logics over Transitive States
[chapter]

2005
*
Lecture Notes in Computer Science
*

The proofs are based on Kruskal's tree theorem and reductions of

doi:10.1007/11532231_14
fatcat:bjvs534zkzc2ff2nyu2zj4k5cq
*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. ...##
###
Towards a Model-Checker for Counter Systems
[chapter]

2006
*
Lecture Notes in Computer Science
*

This paper deals

doi:10.1007/11901914_36
fatcat:v2iri7t2cfcv3phe6unqer6sxq
*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 ...##
###
Memory-efficient algorithms for the verification of temporal properties

1992
*
Formal methods in system design
*

This paper addresses the problem of designing memory-efficient algorithms

doi:10.1007/bf00121128
fatcat:jwvsskomonasrlaffnwrumjgtm
*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 . ...##
###
Checking reachability using matching logic

2012
*
Proceedings of the ACM international conference on Object oriented programming systems languages and applications - OOPSLA '12
*

The proof

doi:10.1145/2384616.2384656
dblp:conf/oopsla/RosuS12
fatcat:jsggbf2tfzh7hepfoagrtd4bge
*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. ...##
###
Memory-Efficient Algorithms for the Verification of Temporal Properties
[chapter]

1992
*
Computer-Aided Verification
*

This paper addresses the problem of designing memory-efficient algorithms

doi:10.1007/978-1-4615-3556-0_5
fatcat:prb4ib6njfc37hjcyfytuanjoi
*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 . ...##
###
A Three-Value Abstraction Technique for the Verification of Epistemic Properties in Multi-agent Systems
[chapter]

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*. ...

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