Mojmír Křetínský

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.

Effective Translation of LTL to Deterministic Rabin Automata: Beyond the (F,G)-Fragment

Some applications of linear temporal logic (LTL) require to translate formulae of the logic to deterministic ω-automata. There are currently two translators producing deterministic automata: ltl2dstar working for the whole LTL and Rabinizer applicable to LTL(F,G) which is the LTL fragment using only modalities F and G. We present a new translation to deterministic Rabin automata via alternating automata and deterministic transition-based generalized Rabin automata. Our translation applies to a fragment that is strictly larger than LTL(F,G). Experimental results show that our algorithm can produce significantly smaller automata compared to Rabinizer and ltl2dstar, especially for more complex LTL formulae.

Compositional Approach to Suspension and Other Improvements to LTL Translation

Recently, there was defined a fragment of LTL (containing fairness properties among other interesting formulae) whose validity over a given infinite word depends only on an arbitrary suffix of the word. Building upon an existing translation from LTL to Buchi automata, we introduce a compositional approach where subformulae of this fragment are translated separately from the rest of an input formula and the produced automata are composed in a way that the subformulae are checked only in relevant accepting strongly connected components of the final automaton. Further, we suggest improvements over some procedures commonly applied to generalized Buchi automata, namely over generalized acceptance simplification and over degeneralization. Finally we show how existing simulation-based reductions can be implemented in a signature-based framework in a way that improves the determinism of the automaton.

Comparison of LTL to Deterministic Rabin Automata Translators

Increasing interest in control synthesis and probabilistic model checking caused recent development of LTL to deterministic ω-automata translation. The standard approach represented by ltl2dstar tool employs Safra’s construction to determinize a Buchi automaton produced by some LTL to Buchi automata translator. Since 2012, three new LTL to deterministic Rabin automata translators appeared, namely Rabinizer, LTL3DRA, and Rabinizer 2. They all avoid Safra’s construction and work on LTL fragments only. We compare performance and automata produced by the mentioned tools, where ltl2dstar is combined with several LTL to Buchi automata translators: besides traditionally used LTL2BA, we also consider LTL− >NBA, LTL3BA, and Spot.

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.

Is there a best büchi automaton for explicit model checking

LTL to Büchi automata (BA) translators are traditionally optimized to produce automata with a small number of states or a small number of non-deterministic states. In this paper, we search for properties of Büchi automata that really influence the performance of explicit model checkers. We do that by manual analysis of several automata and by experiments with common LTL-to-BA translators and realistic verification tasks. As a result of these experiences, we gain a better insight into the characteristics of automata that work well with Spin.

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.