Relating timed and register automata

Timed automata and register automata are well-known models of computation over timed and data words respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can store data values for later comparison. Although these two models behave in appearance differently, several decision problems have the same (un)decidability and complexity results for both models. As a prominent example, emptiness is decidable for alternating automata with one clock or register, both with non-primitive recursive complexity. This is not by chance. This work confirms that there is indeed a tight relationship between the two models. We show that a run of a timed automaton can be simulated by a register automaton, and conversely that a run of a register automaton can be simulated by a timed automaton. Our results allow to transfer complexity and decidability results back and forth between these two kinds of models. We justify the usefulness of these reductions by obtaining new results on register automata.Comment: In Proceedings EXPRESS'10, arXiv:1011.601

A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

Process calculi for service-oriented computing often feature generation of fresh resources. So-called nominal automata have been studied both as semantic models for such calculi, and as acceptors of languages of finite words over infinite alphabets. In this paper we investi-gate nominal automata that accept infinite words. These automata are a generalisation of deterministic Muller automata to the setting of nominal sets. We prove decidability of complement, union, intersection, emptiness and equivalence, and determinacy by ultimately periodic words. The key to obtain such results is to use finite representations of the (otherwise infinite-state) defined class of automata. The definition of such operations enables model checking of process calculi featuring infinite behaviours, and resource allocation, to be implemented using classical automata-theoretic methods

Feasible Automata for Two-Variable Logic with Successor on Data Words

We introduce an automata model for data words, that is words that carry at each position a symbol from a finite alphabet and a value from an unbounded data domain. The model is (semantically) a restriction of data automata, introduced by Bojanczyk, et. al. in 2006, therefore it is called weak data automata. It is strictly less expressive than data automata and the expressive power is incomparable with register automata. The expressive power of weak data automata corresponds exactly to existential monadic second order logic with successor +1 and data value equality \sim, EMSO2(+1,\sim). It follows from previous work, David, et. al. in 2010, that the nonemptiness problem for weak data automata can be decided in 2-NEXPTIME. Furthermore, we study weak B\"uchi automata on data omega-strings. They can be characterized by the extension of EMSO2(+1,\sim) with existential quantifiers for infinite sets. Finally, the same complexity bound for its nonemptiness problem is established by a nondeterministic polynomial time reduction to the nonemptiness problem of weak data automata.Comment: 21 page

A Hypersequent Calculus with Clusters for Data Logic over Ordinals

We study freeze tense logic over well-founded data streams. The logic features past-and future-navigating modalities along with freeze quantifiers, which store the datum of the current position and test data (in)equality later in the formula. We introduce a decidable fragment of that logic, and present a proof system that is sound for the whole logic, and complete for this fragment. Technically, this is a hy-persequent system enriched with an ordering, clusters, and annotations. The proof system is tailored for proof search, and yields an optimal coNP complexity for validity and a small model property for our fragment

Logics on data words

We investigate logics on data words, i.e., words where each position is labelled by some propositions from a finite set and by some data values from an infinite domain. A basic motivation for the study of these logics, called data logics in this work, is that data words are a suitable model to represent traces of concurrent systems with unboundedly many interacting processes. In such representations data values stand for process IDs. Thus, data logics can be used to formulate requirements on such traces. We first study the expressivity and complexity of the satisfiability problem for these logics. Then, we investigate suitable models for concurrent systems with unboundedly many processes. Finally, we analyse the model checking problem for such systems in the case that data logics are used to specify system requirements. One of our main results is that, despite the bad properties of data logics with respect to satisfiability, there are important cases in which model checking with data logics has moderate complexity. Hence, our results motivate for further investigations with the aim to find interesting models and data logics which can be used in practical model checking tools

Safety alternating automata on data words

A data word is a sequence of pairs of a letter from a finite alphabet and an element from an infinite set, where the latter can only be compared for equality. Safety one-way alternating automata with one register on infinite data words are considered, their nonemptiness is shown to be EXPSPACE-complete, and their inclusion decidable but not primitive recursive. The same complexity bounds are obtained for satisfiability and refinement, respectively, for the safety fragment of linear temporal logic with freeze quantification. Dropping the safety restriction, adding past temporal operators, or adding one more register, each causes undecidability