Synchronous Subsequentiality and Approximations to Undecidable Problems

We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an infinite automaton, then most decision problems (apart from membership) still remain undecidable (as they are for synchronous and subsequential rational relations), but on the positive side, they can be approximated in a meaningful way we make precise in this paper. This might make the class useful for some applications, and might serve to establish an intermediate position in the trade-off between issues of expressivity and (un)decidability.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

Model-Checking of Ordered Multi-Pushdown Automata

We address the verification problem of ordered multi-pushdown automata: A multi-stack extension of pushdown automata that comes with a constraint on stack transitions such that a pop can only be performed on the first non-empty stack. First, we show that the emptiness problem for ordered multi-pushdown automata is in 2ETIME. Then, we prove that, for an ordered multi-pushdown automata, the set of all predecessors of a regular set of configurations is an effectively constructible regular set. We exploit this result to solve the global model-checking which consists in computing the set of all configurations of an ordered multi-pushdown automaton that satisfy a given w-regular property (expressible in linear-time temporal logics or the linear-time \mu-calculus). As an immediate consequence, we obtain an 2ETIME upper bound for the model-checking problem of w-regular properties for ordered multi-pushdown automata (matching its lower-bound).Comment: 31 page

Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-semi-decidable problems on these devices such as, for example, emptiness, finiteness, universality, equivalence, etc. These strong negative results trigger the study of subclasses and alternative characterizations of multi-head finite automata for a better understanding of the nature of non-recursive trade-offs and, thus, the borderline between decidable and undecidable problems. In the present paper, we tour a fragment of this literature

Regular Cost Functions, Part I: Logic and Algebra over Words

The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to each input the two values "inside" and "outside". This theory is a continuation of the works on distance automata and similar models. These models of automata have been successfully used for solving the star-height problem, the finite power property, the finite substitution problem, the relative inclusion star-height problem and the boundedness problem for monadic-second order logic over words. Our notion of regularity can be -- as in the classical theory of regular languages -- equivalently defined in terms of automata, expressions, algebraic recognisability, and by a variant of the monadic second-order logic. These equivalences are strict extensions of the corresponding classical results. The present paper introduces the cost monadic logic, the quantitative extension to the notion of monadic second-order logic we use, and show that some problems of existence of bounds are decidable for this logic. This is achieved by introducing the corresponding algebraic formalism: stabilisation monoids.Comment: 47 page

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

A Theory of Partitioned Global Address Spaces

Partitioned global address space (PGAS) is a parallel programming model for the development of applications on clusters. It provides a global address space partitioned among the cluster nodes, and is supported in programming languages like C, C++, and Fortran by means of APIs. In this paper we provide a formal model for the semantics of single instruction, multiple data programs using PGAS APIs. Our model reflects the main features of popular real-world APIs such as SHMEM, ARMCI, GASNet, GPI, and GASPI. A key feature of PGAS is the support for one-sided communication: a node may directly read and write the memory located at a remote node, without explicit synchronization with the processes running on the remote side. One-sided communication increases performance by decoupling process synchronization from data transfer, but requires the programmer to reason about appropriate synchronizations between reads and writes. As a second contribution, we propose and investigate robustness, a criterion for correct synchronization of PGAS programs. Robustness corresponds to acyclicity of a suitable happens-before relation defined on PGAS computations. The requirement is finer than the classical data race freedom and rules out most false error reports. Our main result is an algorithm for checking robustness of PGAS programs. The algorithm makes use of two insights. Using combinatorial arguments we first show that, if a PGAS program is not robust, then there are computations in a certain normal form that violate happens-before acyclicity. Intuitively, normal-form computations delay remote accesses in an ordered way. We then devise an algorithm that checks for cyclic normal-form computations. Essentially, the algorithm is an emptiness check for a novel automaton model that accepts normal-form computations in streaming fashion. Altogether, we prove the robustness problem is PSpace-complete