Paul Gastin

Fast LTL to Büchi Automata Translation

We present an algorithm to generate Buchi automata from LTL formulae. This algorithm generates a very weak alternating co-Buchi automaton and then transforms it into a Buchi automaton, using a generalized Buchi automaton as an intermediate step. Each automaton is simplified on-the-fly in order to save memory and time. As usual we simplify the LTL formula before any treatment. We implemented this algorithm and compared it with Spin: the experiments show that our algorithm is much more efficient than Spin. The criteria of comparison are the size of the resulting automaton, the time of the computation and the memory used. Our implementation is available on the web at the following address: http://verif.liafa.jussieu.fr/ltl2ba

CONCUR 2010 - Concurrency Theory

Dating Concurrent Objects: Real-Time Modeling and Schedulability Analysis.- Applications of Shellable Complexes to Distributed Computing.- Concurrency and Composition in a Stochastic World.- Taming Distributed Asynchronous Systems.- Trust in Anonymity Networks.- Learning I/O Automata.- Constrained Monotonic Abstraction: A CEGAR for Parameterized Verification.- Information Flow in Interactive Systems.- From Multi to Single Stack Automata.- A Geometric Approach to the Problem of Unique Decomposition of Processes.- A Logic for True Concurrency.- A Theory of Design-by-Contract for Distributed Multiparty Interactions.- Bisimilarity of One-Counter Processes Is PSPACE-Complete.- Nash Equilibria for Reachability Objectives in Multi-player Timed Games.- Stochastic Real-Time Games with Qualitative Timed Automata Objectives.- Session Types as Intuitionistic Linear Propositions.- Session Types for Access and Information Flow Control.- Simulation Distances.- Mean-Payoff Automaton Expressions.- Obliging Games.- Multipebble Simulations for Alternating Automata.- Parameterized Verification of Ad Hoc Networks.- Termination in Impure Concurrent Languages.- Buffered Communication Analysis in Distributed Multiparty Sessions.- Efficient Bisimilarities from Second-Order Reaction Semantics for ?-Calculus.- On the Use of Non-deterministic Automata for Presburger Arithmetic.- Reasoning about Optimistic Concurrency Using a Program Logic for History.- Theory by Process.- On the Compositionality of Round Abstraction.- A Linear Account of Session Types in the Pi Calculus.- Generic Forward and Backward Simulations II: Probabilistic Simulation.- Kleene, Rabin, and Scott Are Available.- Reversing Higher-Order Pi.- Modal Logic over Higher Dimensional Automata.- A Communication Based Model for Games of Imperfect Information.- Flat Coalgebraic Fixed Point Logics.- Conditional Automata: A Tool for Safe Removal of Negligible Events.- Representations of Petri Net Interactions.- Communicating Transactions.- Consistent Correlations for Parameterised Boolean Equation Systems with Applications in Correctness Proofs for Manipulations.

Characterization of the expressive power of silent transitions in timed automata

Timed automata are among the most widely studied models for real-time systems. Silent transitions, i.e., e-transitions, have already been proposed in the original paper on timed automata by Alur and Dill [3]. We show that the class TL e of timed languages recognized by automata with e-transitions, is more robust and more expressive than the corresponding class TL without e-transitions. We then focus on e-transitions without reset, i.e. e-transitions which do not reset clocks. We propose an algorithm to construct, given a timed automaton, an equivalent one without such transitions. This algorithm is in two steps, it first suppresses the cycles of e-transitions without reset and then the remaining ones. Then, we prove that a timed automaton such that no e-transition which resets clocks lies on any directed cycle, can be effectively transformed into a timed automaton without etransitions. Interestingly, this main result holds under the assumption of non-Zenoness and it is false otherwise. To complete the picture, we exhibit a simple timed automaton with an e-transition, which resets some clock, on a cycle and which is not equivalent to any e-free timed automaton. To show this, we develop a promising new technique based on the notion of precise action. This paper presents a synthesis of the two conference communications [9] and [13].

A SURVEY ON SMALL FRAGMENTS OF FIRST-ORDER LOGIC OVER FINITE WORDS

We consider fragments of first-order logic over finite words. In particular, we deal with first-order logic with a restricted number of variables and with the lower levels of the alternation hierarchy. We use the algebraic approach to show decidability of expressibility within these fragments. As a byproduct, we survey several characterizations of the respective fragments. We give complete proofs for all characterizations and we provide all necessary background. Some of the proofs seem to be new and simpler than those which can be found elsewhere. We also give a proof of Simons theorem on factorization forests restricted to aperiodic monoids because this is simpler and sufficient for our purpose.

Minimization of Counterexamples in SPIN

We propose an algorithm to find a counterexample to some property in a finite state program. This algorithm is derived from SPIN’s one, but it finds a counterexample faster than SPIN does. In particular it still works in linear time. Compared with SPIN’s algorithm, it requires only one additional bit per state stored. We further propose another algorithm to compute a counterexample of minimal size. Again, this algorithm does not use more memory than SPIN does to approximate a minimal counterexample. The cost to find a counterexample of minimal size is that one has to revisit more states than SPIN. We provide an implementation and discuss experimental results.

Satisfiability and Model Checking for MSO-Definable Temporal Logics Are in PSPACE

Temporal logics over Mazurkiewicz traces have been extensively studied over the past fifteen years. In order to be usable for the verification of concurrent systems they need to have reasonable complexity for the satisfiability and the model checking problems. Whenever a new temporal logic was introduced, a new proof (usually non trivial) was needed to establish the complexity of these problems. In this paper, we introduce a unified framework to define local temporal logics over traces. We prove that the satisfiability problem and the model checking problem for asynchronous Kripke structures for local temporal logics over traces are decidable in PSPACE. This subsumes and sometimes improves all complexity results previously obtained on local temporal logics for traces.

LTL with Past and Two-Way Very-Weak Alternating Automata

In this paper, we propose a translation procedure of PLTL (LTL with past modalities) formulas to Buchi automata using two-way very-weak alternating automata (2VWAA) as an intermiediary step. Our main result is an efficient translation of 2VWAA to generalized Buchi automata (GBA).

Weighted versus Probabilistic Logics

While a mature theory around logics such as MSO, LTL, and CTL has been developed in the pure boolean setting of finite automata, weighted automata lack such a natural connection with (temporal) logic and related verification algorithms. In this paper, we will identify weighted versions of MSO and CTL that generalize the classical logics and even other quantitative extensions such as probabilistic CTL. We establish expressiveness results on our logics giving translations from weighted and probabilistic CTL into weighted MSO.

Pure future local temporal logics are expressively complete for Mazurkiewicz traces

The paper settles a long standing problem for Mazurkiewicz traces: the pure future local temporal logic defined with the basic modalities exists-next and until is expressively complete. This means every first-order definable language of Mazurkiewicz traces can be defined in a pure future local temporal logic. The analogous result with a global interpretation has been known, but the treatment of a local interpretation turned out to be much more involved. Local logics are interesting because both the satisfiability problem and the model checking problem are solvable in PSPACE for these logics whereas they are non-elementary for global logics. Both, the (previously known) global and the (new) local results generalize Kamps Theorem for words, because for sequences local and global viewpoints coincide.

On the Power of Non-Observable Actions in Timed Automata

Timed finite automata, introduced by Alur and Dill, are one of the most widely studied models for real-time systems. We focus in this paper on the power of silent transitions, i.e. e-transitions, in such automata. We show that e-transitions strictly increase the power of timed automata and that the class of timed languages recognized by automata with e-transitions is much more robust than the corresponding class without e-transitions. Our main result shows that these transitions increase the power of these automata only if they reset clocks.