In this paper, we generalize the definitions of transitivity, reflexivity, symmetry, Euclidean and serial properties of relations in the context of a functional approach for temporalmodal logic. The main result is the...
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In this paper, we generalize the definitions of transitivity, reflexivity, symmetry, Euclidean and serial properties of relations in the context of a functional approach for temporalmodal logic. The main result is the proof of definability of these definitions which is obtained by using algebraic characterizations. As a consequence, we will have in our temporalmodal context the generalizations of modal logics T, S4, S5, KD45, etc. These new logics will allow us to establish connections among time flows in very different ways, which enables us to carry out different relations among asynchronous systems. Our further research is focused on the construction of logics with these properties and the design of theorem provers for these logics.
In this paper, we generalize the definitions of transitivity, reflexivity, symmetry, Euclidean and serial properties of relations in the context of a functional approach for temporalmodal logic. The main result is the...
详细信息
In this paper, we generalize the definitions of transitivity, reflexivity, symmetry, Euclidean and serial properties of relations in the context of a functional approach for temporalmodal logic. The main result is the proof of definability of these definitions which is obtained by using algebraic characterizations. As a consequence, we will have in our temporalmodal context the generalizations of modal logics T, S4, S5, KD45, etc. These new logics will allow us to establish connections among time flows in very different ways, which enables us to carry out different relations among asynchronous systems. Our further research is focused on the construction of logics with these properties and the design of theorem provers for these logics.
We consider commutative string rewriting systems (Vector Addition Systems, Petri nets), i.e., string rewriting systems in which all pairs of letters commute. We are interested in reachability: given a rewriting system...
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ISBN:
(纸本)9783540709176
We consider commutative string rewriting systems (Vector Addition Systems, Petri nets), i.e., string rewriting systems in which all pairs of letters commute. We are interested in reachability: given a rewriting system R and words v and w, can v be rewritten to w by applying rules from R? A famous result states that reachability is decidable for commutative string rewriting systems. We show that reachability is decidable for a union of two such systems as well. We obtain, as a special case, that if h : U -> S and g : U -> T are homomorphisms of commutative monoids, then their pushout has a decidable word problem. Finally, we show that, given commutative monoids U, S and T satisfying S boolean AND T = U, it is decidable whether there exists a monoid M such that S boolean OR T subset of M;we also show that the problem remains decidable if we require M to be commutative, too.
We give an explicit coinduction principle for recursively-defined stochastic processes. The principle applies to any closed property, not just equality, and works even when solutions are not unique. The rule encapsula...
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We give an explicit coinduction principle for recursively-defined stochastic processes. The principle applies to any closed property, not just equality, and works even when solutions are not unique. The rule encapsulates low-level analytic arguments, allowing reasoning about such processes at a higher algebraic level. We illustrate the use of the rule in deriving properties of a simple coin-flip process.
First-order translations have recently been characterized as the maps computed by aperiodic single-valued non-deterministic finite transducers (NFTs). It is shown here that this characterization lifts to "V-trans...
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First-order translations have recently been characterized as the maps computed by aperiodic single-valued non-deterministic finite transducers (NFTs). It is shown here that this characterization lifts to "V-translations" and "V-single-valued-NFTs", where V is an arbitrary monoid pseudovariety that is closed under reversal. More strikingly, two-way V-transducers are introduced, and the following three models are shown exactly equivalent to Eilenberg's classical notion of a bimachine when V is a group variety or when V is the variety of aperiodic monoids: V-translations, V-single-valued-NFTs and two-way V-transducers. (c) 2005 Elsevier Inc. All rights reserved.
As specifications and verifications of concurrent systems employ Linear Temporal logic (LTL), it is increasingly likely that logical consequence in LTL will be used in description of computations and parallel reasonin...
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ISBN:
(数字)9783540341680
ISBN:
(纸本)3540341668
As specifications and verifications of concurrent systems employ Linear Temporal logic (LTL), it is increasingly likely that logical consequence in LTL will be used in description of computations and parallel reasoning. We consider the linear temporal logic LTLN, N-1U, B (Z) extending the standard LTL by operations B (before) and N-1 (previous). Two sorts of problems are studied: (i) satisfiability and (ii) description of logical consequence in LTLN, N-1U, B (Z) via admissible logical consecutions (inference rules). The model checking for LTL is a traditional way of studying such logics. Most popular technique based on automata was developed by *** (cf. [39,61). Our paper uses a reduction of logical consecutions and formulas of LTL to consecutions of a uniform form consisting of formulas of temporal degree 1. Based on technique of Kripke structures, we find necessary and sufficient conditions for a consecution to be not admissible in LTLN, N-1U, B (Z). This provides an algorithm recognizing consecutions (rules) admissible in LTLN, N-1U, B (Z) by Kripke structures of size linear in the reduced normal forms of the initial consecutions. As an application, this algorithm solves also the satisfiability problem for LTLN, N-1U, B (Z).
Forbidden Patterns problem (FPP) is a proper generalisation of Constraint Satisfaction Problem (CSP). FPP was introduced in [1] as a combinatorial counterpart of MMSNP, a logic which was in turn introduced in relation...
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ISBN:
(数字)9783540341680
ISBN:
(纸本)3540341668
Forbidden Patterns problem (FPP) is a proper generalisation of Constraint Satisfaction Problem (CSP). FPP was introduced in [1] as a combinatorial counterpart of MMSNP, a logic which was in turn introduced in relation to CSP by Feder and Vardi [2]. We prove that Forbidden Patterns Problems are Constraint Satisfaction Problems when restricted to graphs of bounded degree. This is a generalisation of a result by Haggkvist and Hell who showed that F-moteness of bounded-degree graphs is a CSP (that is, for a given graph F there exists a graph H so that the class of bounded-degree graphs that do not admit a homomorphism from F is exactly the same as the class of bounded-degree graphs that are homomorphic to H). Forbidden-pattern property is a strict generalisation of F-moteness (in fact of F-moteness combined with a CSP) as it involves both vertex- and edge-colourings of the graph F, and thus allows to express NP-complete problems (while F-moteness is always in T). We finally extend our result to arbitrary relational structures, and prove that every problem in MMSNP, restricted to connected inputs of bounded (hyper-graph) degree, is in fact in CSP.
We present an algorithm that-given a set of clauses S saturated under some semantic refinements of the resolution calculus-automatically constructs a Herbrand model M of' S. M is represented by a set of atoms with...
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We present an algorithm that-given a set of clauses S saturated under some semantic refinements of the resolution calculus-automatically constructs a Herbrand model M of' S. M is represented by a set of atoms with equality and disequality constraints interpreted over the finite tree algebra, hence the problem of evaluating first-order formulae in M is decidable. (C) 2003 Elsevier science (USA). All rights reserved.
We show that the class of Event Clock Automata [2] admit a logical characterisation via an unrestricted monadic second order logic interpreted over timed words. The result is interesting in that it provides an unrestr...
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In this paper, we investigate several extensions of the linear time hierarchy (denoted by LTH). We first prove that it is not necessary to erase the oracle tape between two successive oracle calls, thereby lifting a c...
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In this paper, we investigate several extensions of the linear time hierarchy (denoted by LTH). We first prove that it is not necessary to erase the oracle tape between two successive oracle calls, thereby lifting a common restriction on LTH machines. We also define a natural counting extension of LTH and show that it corresponds to a robust notion of counting bounded arithmetic predicates. Finally, we show that the computational power of the majority operator is equivalent to that of the exact counting operator in both contexts. (C) 2002 Elsevier science (USA).
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