A Rice-style theorem for parallel automata

AbstractWe present a general result, similar to Rice’s theorem, concerning the complexity of detecting properties on finite automata enriched by bounded cooperative concurrency, such as statecharts and abstract parallel automata, which we denote by CFAs (Concurrent Finite Automata). On one extreme, the complexity of detecting non-trivial properties that preserve equivalence of machines, i.e. properties of the accepted language, on finite automata, can be as little as O(1). On the other extreme, Rice’s theorem states that all such properties on Turing machines are undecidable. We state that all the non-trivial properties of the regular (or ω-regular) languages, are PSPACE-hard on CFAs with ϵ-moves and on CFAs without ϵ-moves accepting infinite words. We also extend this result to CFAs without ϵ-moves accepting finite words that satisfy a condition that holds for many properties

Winning regions of higher-order pushdown games

International audienceIn this paper we consider parity games defined by higher-order pushdown automata. These automata generalise pushdown automata by the use of higher-order stacks, which are nested ``stack of stacks'' structures. Representing higher-order stacks as well-bracketed words in the usual way, we show that the winning regions of these games are regular sets of words. Moreover a finite automaton recognising this region can be effectively computed. A novelty of our work are abstract pushdown processes which can be seen as (ordinary) pushdown automata but with an infinite stack alphabet. We use the device to give a uniform presentation of our results. From our main result on winning regions of parity games we derive a solution to the Modal Mu-Calculus Global Model-Checking Problem for higher-order pushdown graphs as well as for ranked trees generated by higher-order safe recursion schemes

Abstract Regular Tree Model Checking

International audienceRegular (tree) model checking (RMC) is a promising generic method for formal verification of infinite-state systems. It encodes configurations of systems as words or trees over a suitable alphabet, possibly infinite sets of configurations as finite word or tree automata, and operations of the systems being examined as finite word or tree transducers. The reachability set is then computed by a repeated application of the transducers on the automata representing the currently known set of reachable configurations. In order to facilitate termination of RMC, various acceleration schemas have been proposed. One of them is a combination of RMC with the abstract-check-refine paradigm yielding the so-called abstract regular model checking (ARMC). ARMC has originally been proposed for word automata and transducers only and thus for dealing with systems with linear (or easily linearisable) structure. In this paper, we propose a generalisation of ARMC to the case of dealing with trees which arise naturally in a lot of modelling and verification contexts. In particular, we first propose abstractions of tree automata based on collapsing their states having an equal language of trees up to some bounded height. Then, we propose an abstraction based on collapsing states having a non-empty intersection (and thus "satisfying") the same bottom-up tree "predicate" languages. Finally, we show on several examples that the methods we propose give us very encouraging verification results

On the decidability and complexity of Metric Temporal Logic over finite words

Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL--which includes invariance and time-bounded response properties--is also decidable. These results are quite surprising in that they contradict various claims to the contrary that have appeared in the literature

Event-Clock Nested Automata

In this paper we introduce and study Event-Clock Nested Automata (ECNA), a formalism that combines Event Clock Automata (ECA) and Visibly Pushdown Automata (VPA). ECNA allow to express real-time properties over non-regular patterns of recursive programs. We prove that ECNA retain the same closure and decidability properties of ECA and VPA being closed under Boolean operations and having a decidable language-inclusion problem. In particular, we prove that emptiness, universality, and language-inclusion for ECNA are EXPTIME-complete problems. As for the expressiveness, we have that ECNA properly extend any previous attempt in the literature of combining ECA and VPA