Technical Reports

A List by Author: Mojmír Křetínský

e-mail:
mojmir(a)fi.muni.cz
home page:
http://www.fi.muni.cz/usr/kretinsky/

On Decidability of LTL Model Checking for Weakly Extended Process Rewrite Systems

by Laura Bozzelli, Mojmír Křetínský, Vojtěch Řehák, Jan Strejček, A full version of the paper presented at FSTTCS 2006. November 2006, 27 pages.

FIMU-RS-2006-05. Available as Postscript, PDF.

Abstract:

We establish a decidability boundary of the model checking problem for infinite-state systems defined by Process Rewrite Systems (PRS) or weakly extended Process Rewrite Systems (wPRS), and properties described by basic fragments of action-based Linear Temporal Logic (LTL). It is known that the problem for general LTL properties is decidable for Petri nets and for pushdown processes, while it is undecidable for PA processes. As our main result, we show that the problem is decidable for wPRS if we consider properties defined by formulae with only modalities strict eventually and strict always. Moreover, we show that the problem remains undecidable for PA processes even with respect to the LTL fragment with the only modality until or the fragment with modalities next and infinitely often.

Refining the Undecidability Border of Weak Bisimilarity

by Mojmír Křetínský, Vojtěch Řehák, Jan Strejček, A full version of the paper presented at INFINITY 2005. August 2005, 20 pages.

FIMU-RS-2005-06. Available as Postscript, PDF.

Abstract:

Weak bisimilarity is one of the most studied behavioural equivalences. This equivalence is undecidable for pushdown processes (PDA), process algebras (PA), and multiset automata (MSA, also known as parallel pushdown processes, PPDA). Its decidability is an open question for basic process algebras (BPA) and basic parallel processes (BPP). We move the undecidability border towards these classes by showing that the equivalence remains undecidable for weakly extended versions of BPA and BPP. Further, we show the results hold for even more restricted classes of normed BPA with finite constraint system and normed BPP with finite constraint system.

Process Rewrite Systems with Weak Finite-State Unit

by Mojmír Křetínský, Vojtěch Řehák, Jan Strejček, This is a full version of the paper presented at INFINITY`03. September 2003, 23 pages.

FIMU-RS-2003-05. Available as Postscript, PDF.

Abstract:

Various classes of infinite-state processes are often specified by rewrite systems. We extend Mayr`s Process Rewrite Systems (PRS) by finite-state unit whose transition function satisfies some restrictions inspired by weak finite automata. We classify these models by their expressiveness and show how the hierarchy of new classes (w.r.t. bisimilarity) is related to both PRS hierarchy of Mayr and two other hierarchies of PRS extensions introduced in [JKM02, Str02].

A Fully Abstract Semantics for a Version of Synchronous Concurrent Constraint Programming

by Jean-Marie Jacquet, Luboš Brim, David Gilbert, Mojmír Křetínský, December 1999, 62 pages.

FIMU-RS-99-08. Available as Postscript, PDF.

Abstract:

Concurrent constraint programming is classically based on asynchronous communication via a shared store. In previous work, we presented a new version of the ask and tell primitives which features synchronicity, our approach being based on the idea of telling new information just in the case that a concurrently running process is asking for it. We turn in this paper to a semantic study of this new framework, called Scc.

It is first shown to be different in nature from classical concurrent constraint programming and from CCS, a classical reference in traditional concurrency theory. This suggests the interest of new semantics for Scc. To that end, an operational semantics reporting the steps of the computations is presented. A denotational semantics is then proposed. It uses monotonic sequences of labelled pairs of input-output states, possibly containing gaps, and ending - according to the logic programming tradition - with marks reporting success or failure. This denotational semantics is proved to be correct with respect to the operational semantics as well as fully abstract.

MFCS`98 Workshop on Concurrency - Preproceedings

by Petr Jančar, Mojmír Křetínský, Pre-proceedings of the MFCS`98 Workshop on Concurrency (the PS file is NOT provided, as it is too large (approx. 30MB); take pdf (3.5 MB) instead). July 1998, 209 pages.

FIMU-RS-98-06. Available as Postscript, PDF.

Abstract:

This volume contains the pre-proceedings of the MFCS`98 Workshop on Concurrency, which took place in Brno, Czech Republic, August 27-29, 1998, as a satellite event of the 23rd international symposium on Mathematical Foundations of Computer Science. It is composed of two invited papers delivered by Javier Esparza (Munich) and Faron Moller (Uppsala), and of 17 contributed papers selected out of 24 submissions. The revised (and full) version of the proceedings should appear as a volume of Electronic Notes in Theoretical Computer Science (Elsevier).

Comparing Expressibility of Normed BPA and Normed BPP Processes

by Ivana Černá, Mojmír Křetínský, Antonín Kučera, This is a full version of the paper which is to be presented at CSL`96. June 1996, 28 pages.

FIMU-RS-96-02. Available as Postscript, PDF.

Abstract:

We compare the classes of behaviours (transition systems) which can be generated by normed BPA_{\tau} and normed BPP_{\tau} processes. We exactly classify the intersection of these two classes, i.e., the class of transition systems which can be equivalently (up to bisimilarity) described by the syntax of normed BPA_{\tau} and normed BPP_{\tau} processes. We provide such a characterisation for classes of normed BPA and normed BPP processes as well.

Next we show that it is decidable in polynomial time whether for a given normed BPA_{\tau} (or BPP_{\tau} respectively) process X there is some (unspecified) normed BPP_{\tau} (or BPA_{\tau} respectively) process X` such that X is bisimilar to X`. Moreover, if the answer is positive then our algorithms also construct the process X`. Simplified versions of the algorithms mentioned above for normed BPA and normed BPP are given too.

As an immediate (but important) consequence we also obtain the decidability of bisimilarity in the union of normed BPA_{\tau} and normed BPP_{\tau} processes.

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