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Characterizing finite Kripke structures in propositional temporal logic

M.C. Browne, E.M. Clarke, O. Grümberg
1988 Theoretical Computer Science  
Our proof involves showing that, for any 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).  ... 
doi:10.1016/0304-3975(88)90098-9 fatcat:6uwyam3bgzdixpr2wxievretoq

Characterizing Kripke structures in temporal logic [chapter]

M. C. Browne, E. M. Clarke, O. Grümberg
1987 Lecture Notes in Computer Science  
Our goal is to show that for any 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.  ... 
doi:10.1007/3-540-17660-8_60 fatcat:mc24m7ewynemvl4gmaggwvls2e

Systematic Construction of Temporal Logics for Dynamical Systems via Coalgebra [article]

Baltasar Trancón y Widemann
2012 arXiv   pre-print
Lastly, the resulting systems are 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.  ... 
arXiv:1212.1734v1 fatcat:yvtvvaxkrfbzjosqzjopixpg2q

From Model-Checking to Temporal Logic Constraint Solving [chapter]

François Fages, Aurélien Rizk
2009 Lecture Notes in Computer Science  
This allows us to define a continuous degree of satisfaction for a 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.  ... 
doi:10.1007/978-3-642-04244-7_26 fatcat:woxsmrefkja4fn7grsp2h32ny4

Model Checking Partial State Spaces with 3-Valued Temporal Logics [chapter]

Glenn Bruns, Patrice Godefroid
1999 Lecture Notes in Computer Science  
We define a preorder on partial 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.  ... 
doi:10.1007/3-540-48683-6_25 fatcat:ohs4zg3omnfnlefniq4pahqynu

Deriving Inverse Operators for Modal Logic [chapter]

Michell Guzmán, Salim Perchy, Camilo Rueda, Frank D. Valencia
2016 Lecture Notes in Computer Science  
We shall apply our results to existing modal languages such as the weakest normal modal 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.  ... 
doi:10.1007/978-3-319-46750-4_13 fatcat:v3arqrxk4fbfhbinp6s2egb2rm

Towards Systematic Construction of Temporal Logics for Dynamical Systems via Coalgebra [chapter]

Baltasar Trancón y Widemann
2014 Lecture Notes in Computer Science  
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.  ...  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  ... 
doi:10.1007/978-3-662-44124-4_12 fatcat:cubjy7rqe5dk3akiovnbyccmv4

Equivalences for fair Kripke structures [chapter]

Adnan Aziz, Vigyan Singhal, Felice Balarin, Robert K. Brayton, Alberto L. Sangiovanni-Vincentelli
1994 Lecture Notes in Computer Science  
As a consequence of our proof, we also obtain 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.  ... 
doi:10.1007/3-540-58201-0_82 fatcat:zblt34vvqzhrfbrfqjbdzrqrry

Linear temporal logic with until and next, logical consecutions

V. Rybakov
2008 Annals of Pure and Applied Logic  
These conditions lead to an algorithm which recognizes consecutions (rules) admissible 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] .  ... 
doi:10.1016/j.apal.2008.03.001 fatcat:ycdiicbpgba5naz4e4a3j5hr3y

Weak Kripke Structures and LTL [chapter]

Lars Kuhtz, Bernd Finkbeiner
2011 Lecture Notes in Computer Science  
We show that the classic PSPACE-hardness result is actually limited to a subclass of the 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.  ... 
doi:10.1007/978-3-642-23217-6_28 fatcat:kujebsdzfbamjdkagplit3dzwq

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  ... 

Complexity of ITL Model Checking: Some Well-Behaved Fragments of the Interval Logic HS

Alberto Molinari, Angelo Montanari, Adriano Peron
2015 2015 22nd International Symposium on Temporal Representation and Reasoning (TIME)  
Recently, a non-elementary model checking algorithm for Halpern and Shoham's modal 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  ... 
doi:10.1109/time.2015.12 dblp:conf/time/MolinariMP15 fatcat:63ad2aqvnra4nil3nqup4376i4

On the Complexity of Semantic Self-minimization

Adam Antonik, Michael Huth
2009 Electronical Notes in Theoretical Computer Science  
Partial 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.  ... 
doi:10.1016/j.entcs.2009.08.002 fatcat:7k3vfxh23rbhzfp53gcabjdvty

Model Checking with Multi-valued Logics [chapter]

Glenn Bruns, Patrice Godefroid
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.  ... 
doi:10.1007/978-3-540-27836-8_26 fatcat:nvnxsj7yirffbiivmvez3ume6u

Interval vs. Point Temporal Logic Model Checking

Laura Bozzelli, Alberto Molinari, Angelo Montanari, Adriano Peron, Pietro Sala
2018 ACM Transactions on Computational Logic  
The behavior of the system is modeled by means of (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.  ... 
doi:10.1145/3281028 fatcat:vvskrfjngvf7niro33b6amoolq
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