When Are Prime Formulae Characteristic?

Aceto, Luca; Monica, Dario Della; Fábregas, Ignacio; Ingólfsdóttir, Anna

doi:10.1007/978-3-662-48057-1_6

Cited by 5 publications

(8 citation statements)

References 14 publications

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“…This construction allows one to verify that two CCS processes are equivalent by reducing this problem to model checking. Similar constructions were studied later in [18,22] for instance and in a more general manner in [1,2].…”

Section: Introductionmentioning

confidence: 65%

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The Completeness Problem for Modal Logic

Achilleos

2017

Logical Foundations of Computer Science

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We introduce the completeness problem for Modal Logic and examine its complexity. For a definition of completeness for formulas, given a formula of a modal logic, the completeness problem asks whether the formula is complete for that logic. We discover that completeness and validity have the same complexity -with certain exceptions for which there are, in general, no complete formulas. To prove upper bounds, we present a non-deterministic polynomial-time procedure with an oracle from PSPACE that combines tableaux and a test for bisimulation, and determines whether a formula is complete.

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Section: Introductionmentioning

confidence: 65%

“…frame (W, R)) finite if W is finite. 1 If M is a model (for logic l) and a is a state of M, then (M, a) is a pointed model (resp. for l).…”

Section: Modal Logicmentioning

confidence: 99%

The Completeness Problem for Modal Logic

Achilleos

2017

Logical Foundations of Computer Science

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“…On the other hand, we get an operational characterization of logical equivalences. The importance of modal logical characterization for behavioural equivalences has been explained in [1], in particular, the resulting capabilities to express distinguishing formulas for automatic verification of systems and characteristic formulas for the equivalence classes of processes [2], to demonstrate finitariness and algebraicity of behavioural preorders, as well as to give a testing interpretation of bisimulation equivalence [59]. Logical characterization of bisimulation equivalence guarantees that the validity of all logical formulas is preserved while quotienting (by the equivalence) the state space before model checking, thereby simplifying verification of behavioural properties [9,69,24].…”

Section: Logical Characterizationmentioning

confidence: 99%

Logical characterization of fluid equivalences

Tarasyuk¹,

Buchholz²

2019

Sib. Elektron. Mat. Izv.

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We investigate fluid equivalences that allow one to compare and reduce behaviour of labeled fluid stochastic Petri nets (LFSPNs) with a single continuous place while preserving their discrete and continuous properties. We propose a linear-time relation of fluid trace equivalence and its branching-time counterpart, fluid bisimulation equivalence. Both fluid relations take into account the essential features of the LFSPNs behaviour, such as functional activity, stochastic timing and fluid flow. We consider the LFSPNs whose continuous markings have no influence to the discrete ones, i.e. every discrete marking determines completely both the set of enabled transitions, their firing rates and the fluid flow rates of the incoming and outgoing arcs for each continuous place. Moreover, we require that the discrete part of the LFSPNs should be continuous time stochastic Petri nets. The underlying stochastic model for the discrete part of the LFSPNs is continuous time Markov chains (CTMCs). The performance analysis of the continuous part of LFSPNs is accomplished via the associated stochastic fluid models (SFMs). We characterize logically fluid trace and bisimulation equivalences with two novel fluid modal logics HM L f lt and HM L f lb , constructed on the basis of the well-known Hennessy-Milner Logic (HML). These characterizations guarantee that two LFSPNs are fluid (trace or bisimulation) equivalent iff they satisfy the same formulas of the respective logic, i.e. they are logically equivalent. The results imply operational characterizations of the logical equivalences.

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Section: Logical Characterization Of the Fluid Equivalencesmentioning

confidence: 99%

Behavioural equivalences for fluid stochastic Petri nets

Tarasyuk¹,

Buchholz²

2017

Preprint

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We propose fluid equivalences that allow one to compare and reduce behaviour of labeled fluid stochastic Petri nets (LFSPNs) while preserving their discrete and continuous properties. We define a linear-time relation of fluid trace equivalence and its branching-time counterpart, fluid bisimulation equivalence. Both fluid relations take into account the essential features of the LFSPNs behaviour, such as functional activity, stochastic timing and fluid flow. We consider the LFSPNs whose continuous markings have no influence to the discrete ones, i.e. every discrete marking determines completely both the set of enabled transitions, their firing rates and the fluid flow rates of the incoming and outgoing arcs for each continuous place. Moreover, we require that the discrete part of the LFSPNs should be continuous time stochastic Petri nets. The underlying stochastic model for the discrete part of the LFSPNs is continuous time Markov chains (CTMCs). The performance analysis of the continuous part of LFSPNs is accomplished via the associated stochastic fluid models (SFMs).We show that fluid trace equivalence preserves average potential fluid change volume for the transition sequences of every certain length. We prove that fluid bisimulation equivalence preserves the following aggregated (by such a bisimulation) probability functions: stationary probability mass for the underlying CTMC, as well as stationary fluid buffer empty probability, fluid density and distribution for the associated SFM. Hence, the equivalence guarantees identity of a number of discrete and continuous performance measures. Fluid bisimulation equivalence is then used to simplify the qualitative and quantitative analysis of LFSPNs that is accomplished by means of quotienting (by the equivalence) the discrete reachability graph and underlying CTMC. To describe the quotient associated SFM, the quotients of the probability functions are defined. We also characterize logically fluid trace and bisimulation equivalences with two novel fluid modal logics HM L f lt and HM L f lb , constructed on the basis of the well-known Hennessy-Milner Logic HML. These results can be seen as operational characterizations of the corresponding logical equivalences. The application example of a document preparation system demonstrates the behavioural analysis via quotienting by fluid bisimulation equivalence.

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When Are Prime Formulae Characteristic?

Cited by 5 publications

References 14 publications

The Completeness Problem for Modal Logic

The Completeness Problem for Modal Logic

Logical characterization of fluid equivalences

Behavioural equivalences for fluid stochastic Petri nets

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