Vojtěch Řehák

LTL to büchi automata translation: fast and more deterministic

We introduce improvements in the algorithm by Gastin and Oddoux translating LTL formulae into Buchi automata via very weak alternating co-Buchi automata and generalized Buchi automata. Several improvements are based on specific properties of any formula where each branch of its syntax tree contains at least one eventually operator and at least one always operator. These changes usually result in faster translations and smaller automata. Other improvements reduce non-determinism in the produced automata. In fact, we modified all the steps of the original algorithm and its implementation known as LTL2BA. Experimental results show that our modifications are real improvements. Their implementations within an LTL2BA translation made LTL2BA very competitive with the current version of SPOT, sometimes outperforming it substantially.

Extended Process Rewrite Systems: Expressiveness and reachability

We unify a view on three extensions of Process Rewrite Systems (PRS) and compare their expressive power with that of PRS. We show that the class of Petri nets is less expressive up to bisimulation equivalence than the class of PA processes extended with a finite state control unit. Further we show our main result that the reachability problem for PRS extended with a so called weak finite state unit is decidable.

Verification of Open Interactive Markov Chains

Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation. For this we embed the IMC into a game that is played with the environment. We devise algorithms that enable us to derive bounds on reachability probabilities that are assured to hold in any composition context.

Reachability of hennessy-milner properties for weakly extended PRS

We examine the problem whether a given weakly extended process rewrite system (wPRS) contains a reachable state satisfying a given formula of Hennessy–Milner logic. We show that this problem is decidable. As a corollary we observe that the problem of strong bisimilarity between wPRS and finite-state systems is decidable. Decidability of the same problem for wPRS subclasses, namely PAN and PRS, has been formulated as an open question, see e.g. [Srb02]. We also strengthen some related undecidability results on some PRS subclasses.

On Extensions of Process Rewrite Systems: Rewrite Systems with Weak Finite-State Unit

Various classes of infinite-state processes are often specified by rewrite systems. We extend Mayrs 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.

Fixed-delay events in generalized semi-Markov processes revisited

We study long run average behavior of generalized semi-Markov processes with both fixed-delay events as well as variable-delay events. We show that allowing two fixed-delay events and one variable-delay event may cause an unstable behavior of a GSMP. In particular, we show that a frequency of a given state may not be defined for almost all runs (or more generally, an invariant measure may not exist). We use this observation to disprove several results from literature. Next we study GSMP with at most one fixed-delay event combined with an arbitrary number of variable-delay events. We prove that such a GSMP always possesses an invariant measure which means that the frequencies of states are always well defined and we provide algorithms for approximation of these frequencies. Additionally, we show that the positive results remain valid even if we allow an arbitrary number of reasonably restricted fixed-delay events.

Dealing with Zero Density Using Piecewise Phase-Type Approximation

Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC is needed for some standard distributions, in particular most distributions with regions of zero density such as uniform or shifted distributions. Addressing this class of distributions, we suggest an alternative representation by CTMC extended with discrete-time transitions. Using discrete-time transitions we split the density function into multiple intervals. Within each interval, we then approximate the density with standard phase-type fitting. We provide an experimental evidence that our method requires only a moderate number of states to approximate such distributions with regions of zero density. Furthermore, the usage of CTMC with discrete-time transitions is supported by a number of techniques for their analysis. Thus, our results promise an efficient approach to the transient analysis of a class of non-Markovian models.

Almost linear büchi automata

We introduce a new fragment of linear temporal logic (LTL) called LIO and a new class of Buchi automata (BA) called almost linear Buchi automata (ALBA). We provide effective translations between LIO and ALBA showing that the two formalisms are expressively equivalent. As we expect there to be applications of our results in model checking, we use two standard sources of specification formulae, namely Spec Patterns and BEEM, to study the practical relevance of the LIO fragment, and to compare our translation of LIO to ALBA with two standard translations of LTL to BA using alternating automata. Finally, we demonstrate that the LIO to ALBA translation can be much faster than the standard translation, and the resulting automata can be substantially smaller.

On decidability of LTL model checking for process rewrite systems

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.

On Decidability of LTL+Past Model Checking for Process Rewrite Systems

The paper [Bozzelli, L., M. Kretinsky, V. Rehak and J. Strejcek, On decidability of LTL model checking for process rewrite systems, in: FSTTCS 2006, LNCS 4337 (2006), pp. 248-259] shows that the model checking problem for (weakly extended) Process Rewrite Systems and properties given by LTL formulae with temporal operators strict eventually and strict always is decidable. The same paper contains an open question whether the problem remains decidable even if we extend the set of properties by allowing also past counterparts of the mentioned operators. The current paper gives a positive answer to this question.