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Characterizing finite Kripke structures in propositional temporal logic

1988
*
Theoretical Computer Science
*

Our proof involves showing that, for any

doi:10.1016/0304-3975(88)90098-9
fatcat:6uwyam3bgzdixpr2wxievretoq
*finite**Kripke**structure*M, it is possible to construct a CTL formula FM that uniquely*characterizes*M. ... We also give a polynomial algorithm for determining if two*structures*are stuttering equivalent and discuss the relevance of our results for*temporal**logic*model checking and synthesis procedures. ...*In*linear*temporal**logic*, operators are provided for describing events along a single time path (i.e., along a single path*in*a*Kripke**structure*). ...##
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Characterizing Kripke structures in temporal logic
[chapter]

1987
*
Lecture Notes in Computer Science
*

Our goal is to show that for any

doi:10.1007/3-540-17660-8_60
fatcat:mc24m7ewynemvl4gmaggwvls2e
*finite**Kripke**structure*M, it is possible to construct a CTL formula F M that uniquely*characterizes*M. ...*In*linear*temporal**logic*, operators are provided for desclibing events along a single time path (i.e., along a single path*in*a*Kripke**structure*). ... Our results show that (at least*in*theory) no such extension is necessary for branching-time*temporal**logic*. Any*Kripke**structure*can be specified directly by a formula of branching-time*logic*. ...##
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Systematic Construction of Temporal Logics for Dynamical Systems via Coalgebra
[article]

2012
*
arXiv
*
pre-print

Lastly, the resulting systems are

arXiv:1212.1734v1
fatcat:yvtvvaxkrfbzjosqzjopixpg2q
*characterized*with respect to the*temporal*properties they express. ... Here, a systematic approach to the construction of*temporal**logics*for dynamical systems is proposed: Firstly, it is noted that dynamical systems can be seen as coalgebras*in*various ways. ... A*propositional*modal*logic*L is said to have the*finite*model property, if and only if it is complete for a class of*finite**Kripke*frames. Theorem 16. ...##
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From Model-Checking to Temporal Logic Constraint Solving
[chapter]

2009
*
Lecture Notes in Computer Science
*

This allows us to define a continuous degree of satisfaction for a

doi:10.1007/978-3-642-04244-7_26
fatcat:woxsmrefkja4fn7grsp2h32ny4
*temporal**logic*formula*in*a given*structure*, opening up the field of model-checking to optimization. ...*In*this paper, we show how model-checking can be generalized to*temporal**logic*constraint solving, by considering*temporal**logic*formulae with free variables over some domain D, and by computing a validity ... QFCTL Model-Checking Algorithm The (global) model-checking problem is the problem of determining the set of states*in*which a given*temporal**logic*formula is true*in*a given*finite**Kripke**structure*. ...##
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Model Checking Partial State Spaces with 3-Valued Temporal Logics
[chapter]

1999
*
Lecture Notes in Computer Science
*

We define a preorder on partial

doi:10.1007/3-540-48683-6_25
fatcat:ohs4zg3omnfnlefniq4pahqynu
*Kripke**structures*that reflects their degree of completeness. We then provide a*logical**characterization*of this preorder. ... We represent incomplete state spaces as partial*Kripke**structures*, and give a 3-valued interpretation to modal*logic*formulas on these*structures*. ...*Kripke**Structures*and Modal*Logic*Let P be a nonempty*finite*set of atomic*propositions*. Definition 1. ...##
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Deriving Inverse Operators for Modal Logic
[chapter]

2016
*
Lecture Notes in Computer Science
*

We shall apply our results to existing modal languages such as the weakest normal modal

doi:10.1007/978-3-319-46750-4_13
fatcat:v3arqrxk4fbfhbinp6s2egb2rm
*logic*, Hennessy-Milner*logic*, and linear-time*temporal**logic*. ... We shall use spatial constraint systems to give an abstract*characterization*of the notion of normality*in*modal*logic*and to derive right inverse/reverse operators for modal languages. ... We shall also give an algebraic*characterization*of the modal*logic*notion of normality as maps that preserve*finite*suprema. ...##
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Towards Systematic Construction of Temporal Logics for Dynamical Systems via Coalgebra
[chapter]

2014
*
Lecture Notes in Computer Science
*

Here, a systematic approach to the construction of

doi:10.1007/978-3-662-44124-4_12
fatcat:cubjy7rqe5dk3akiovnbyccmv4
*temporal**logics*for dynamical systems is proposed: Firstly, it is noted that dynamical systems can be seen as coalgebras*in*various ways. ... Note that being symmetric*in*this sense is different from being Abelian.*In*fact, symmetry*characterizes*a famous subclass of monoids, namely the groups: Lemma 1 (Groups). ... A*Kripke*model (of*propositional*modal*logic*) is an extended*structure*(W, R, ), where is a relation between W and the language Form of*logical*formulas, such that: w ¬A ⇐⇒ w A w A → B ⇐⇒ w A implies w ...##
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Equivalences for fair Kripke structures
[chapter]

1994
*
Lecture Notes in Computer Science
*

As a consequence of our proof, we also obtain

doi:10.1007/3-540-58201-0_82
fatcat:zblt34vvqzhrfbrfqjbdzrqrry
*characterizations*of states*in*the fair*structure**in*terms of CTL* and CTL formulae. ... We extend the notion of bisimulation to*Kripke**structures*with fairness. We define equivalences that preserve fairness and are akin to bisimulation. ... Browne, Clarke and Grfimberg [2]*characterized**finite**Kripke**structures**in**temporal**logic*. ...##
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Linear temporal logic with until and next, logical consecutions

2008
*
Annals of Pure and Applied Logic
*

These conditions lead to an algorithm which recognizes consecutions (rules) admissible

doi:10.1016/j.apal.2008.03.001
fatcat:ycdiicbpgba5naz4e4a3j5hr3y
*in*LT L by verifying the validity of consecutions*in*special*finite**Kripke**structures*of size square polynomial*in*... We start by a simple reduction of*logical*consecutions (inference rules) of LT L to equivalent ones*in*the reduced normal form (which have uniform*structure*and consist of formulas of*temporal*degree 1 ... The preliminary results of this paper were reported at conferences CSR2006, Moscow, 2006 [32] and*Logical*Foundations of Computer Science, New York, 2007 [33] . ...##
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Weak Kripke Structures and LTL
[chapter]

2011
*
Lecture Notes in Computer Science
*

We show that the classic PSPACE-hardness result is actually limited to a subclass of the

doi:10.1007/978-3-642-23217-6_28
fatcat:kujebsdzfbamjdkagplit3dzwq
*Kripke*frames, which is*characterized*by a simple*structural*condition: the model checking problem is only PSPACE-hard ... We revisit the complexity of the model checking problem for formulas of linear-time*temporal**logic*(LTL). ... Introduction Model checking, the automatic verification of a*finite*-state*structure*against a formula of a*temporal**logic*, is one of the key advances*in*systems theory over the past decades. ...##
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Page 5921 of Mathematical Reviews Vol. , Issue 89K
[page]

1989
*
Mathematical Reviews
*

M. (1-CMU-C);
Griimberg, O. (1-CMU-C)

*Characterizing**finite**Kripke**structures**in**propositional**temporal**logic*. ... The goal of the paper is to show that for any*finite**Kripke**structure*(FKS), i.e., a labelled state-transition graph with an initial state, it is possible to construct a CTL formula uniquely*characterizing*...##
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Complexity of ITL Model Checking: Some Well-Behaved Fragments of the Interval Logic HS

2015
*
2015 22nd International Symposium on Temporal Representation and Reasoning (TIME)
*

Recently, a non-elementary model checking algorithm for Halpern and Shoham's modal

doi:10.1109/time.2015.12
dblp:conf/time/MolinariMP15
fatcat:63ad2aqvnra4nil3nqup4376i4
*logic*of time intervals HS over*finite**Kripke**structures*(under the homogeneity assumption) and an EXPSPACE model checking ... Most of the proposed solutions make use of classical, point-based*temporal**logics*, while little work has been done*in*the interval*temporal**logic*setting. ...*In*the standard formulation, systems are described as (*finite*) labelled state-transition graphs (*Kripke**structures*) and point-based, linear or branching*temporal**logics*(e.g., LTL or CTL) are used to constrain ...##
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On the Complexity of Semantic Self-minimization

2009
*
Electronical Notes in Theoretical Computer Science
*

Partial

doi:10.1016/j.entcs.2009.08.002
fatcat:7k3vfxh23rbhzfp53gcabjdvty
*Kripke**structures*model only parts of a state space and so enable aggressive abstraction of systems prior to verifying them with respect to a formula of*temporal**logic*. ...*In*this paper we provide a systematic study of the complexity of deciding whether a formula of*propositional**logic*,*propositional*modal*logic*or the*propositional*modal mu-calculus is semantically self-minimizing ... Since all*temporal**logics*we study enjoy a*finite*-model property (and since we wish to verify abstractions that have*finite*state space), we will work with*finite*-state models throughout this paper. ...##
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Model Checking with Multi-valued Logics
[chapter]

2004
*
Lecture Notes in Computer Science
*

*In*multi-valued model checking, a

*temporal*

*logic*formula is interpreted relative to a

*structure*not as a truth value but as a lattice element. ...

*In*this paper we present new algorithms for multi-valued model checking. ... This work was funded

*in*part by NSF CCR-0341658. ...

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Interval vs. Point Temporal Logic Model Checking

2018
*
ACM Transactions on Computational Logic
*

The behavior of the system is modeled by means of (

doi:10.1145/3281028
fatcat:vvskrfjngvf7niro33b6amoolq
*finite*)*Kripke**structures*, as usual. ...*In*the last years, model checking with interval*temporal**logics*is emerging as a viable alternative to model checking with standard point-based*temporal**logics*, such as LTL, CTL, CTL*, and the like. ... Acknowledgments The work by Alberto Molinari, Angelo Montanari, and Pietro Sala has been supported by the GNCS project*Logic*and Automata for Interval Model Checking. ...
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