Reachability analysis of first-order definable pushdown systems

We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures. Moreover, for the more restrictive homogeneous structures, we are able to give concrete complexity upper bounds. We show ample applicability of our technique by presenting several concrete examples of homogeneous structures, subsuming, with optimal complexity, known results from the literature. We show that infinitely many such examples of homogeneous structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1

Model checking usage policies

We study usage automata, a formal model for specifying policies on the usage of resources. Usage automata extend finite state automata with some additional features, parameters and guards, that improve their expressivity. We show that usage automata are expressive enough to model policies of real-world applications. We discuss their expressive power, and we prove that the problem of telling whether a computation complies with a usage policy is decidable. The main contribution of this paper is a model checking technique for usage automata. The model is that of usages, i.e. basic processes that describe the possible patterns of resource access and creation. In spite of the model having infinite states, because of recursion and resource creation, we devise a polynomial-time model checking technique for deciding when a usage complies with a usage policy

Rigid Tree Automata and Applications

International audienceWe introduce the class of Rigid Tree Automata (RTA), an extension of standard bottom-up automata on ranked trees with distinguished states called rigid. Rigid states define a restriction on the computation of RTA on trees: RTA can test for equality in subtrees reaching the same rigid state. RTA are able to perform local and global tests of equality between subtrees, non-linear tree pattern matching, and some inequality and disequality tests as well. Properties like determinism, pumping lemma, Boolean closure, and several decision problems are studied in detail. In particular, the emptiness problem is shown decidable in linear time for RTA whereas membership of a given tree to the language of a given RTA is NP-complete. Our main result is the decidability of whether a given tree belongs to the rewrite closure of an RTA language under a restricted family of term rewriting systems, whereas this closure is not an RTA language. This result, one of the first on rewrite closure of languages of tree automata with constraints, is enabling the extension of model checking procedures based on finite tree automata techniques, in particular for the verification of communicating processes with several local non rewritable memories, like security protocols. Finally, a comparison of RTA with several classes of tree automata with local and global equality tests, with dag automata and Horn clause formalisms is also provided

Algebraic hierarchical decomposition of finite state automata : a computational approach

The theory of algebraic hierarchical decomposition of finite state automata is an important and well developed branch of theoretical computer science (Krohn-Rhodes Theory). Beyond this it gives a general model for some important aspects of our cognitive capabilities and also provides possible means for constructing artificial cognitive systems: a Krohn-Rhodes decomposition may serve as a formal model of understanding since we comprehend the world around us in terms of hierarchical representations. In order to investigate formal models of understanding using this approach, we need efficient tools but despite the significance of the theory there has been no computational implementation until this work. Here the main aim was to open up the vast space of these decompositions by developing a computational toolkit and to make the initial steps of the exploration. Two different decomposition methods were implemented: the VuT and the holonomy decomposition. Since the holonomy method, unlike the VUT method, gives decompositions of reasonable lengths, it was chosen for a more detailed study. In studying the holonomy decomposition our main focus is to develop techniques which enable us to calculate the decompositions efficiently, since eventually we would like to apply the decompositions for real-world problems. As the most crucial part is finding the the group components we present several different ways for solving this problem. Then we investigate actual decompositions generated by the holonomy method: automata with some spatial structure illustrating the core structure of the holonomy decomposition, cases for showing interesting properties of the decomposition (length of the decomposition, number of states of a component), and the decomposition of finite residue class rings of integers modulo n. Finally we analyse the applicability of the holonomy decompositions as formal theories of understanding, and delineate the directions for further research

An algorithm for recognition of n-collapsing words

AbstractA word w over a finite alphabet Σ is n-collapsing if for an arbitrary deterministic finite automaton A=〈Q,Σ,δ〉, the inequality |δ(Q,w)|≤|Q|−n holds provided that |δ(Q,u)|≤|Q|−n for some word u∈Σ+ (depending on A). We prove that the property of n-collapsing is algorithmically recognizable for any given positive integer n. We also prove that the language of all n-collapsing words is context-sensitive