Tightening the Complexity of Equivalence Problems for Commutative Grammars

We show that the language equivalence problem for regular and context-free commutative grammars is coNEXP-complete. In addition, our lower bound immediately yields further coNEXP-completeness results for equivalence problems for communication-free Petri nets and reversal-bounded counter automata. Moreover, we improve both lower and upper bounds for language equivalence for exponent-sensitive commutative grammars.Comment: 21 page

Integer Vector Addition Systems with States

This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof. A ZVASS comprises a finite-state controller with a finite number of counters ranging over the integers. Although it is folklore that reachability in ZVASS is NP-complete, it turns out that despite their naturalness, from a complexity point of view this class has received little attention in the literature. We fill this gap by providing an in-depth analysis of the computational complexity of the aforementioned decision problems. Most interestingly, it turns out that while the addition of reset operations to ordinary VASS leads to undecidability and Ackermann-hardness of reachability and coverability, respectively, they can be added to ZVASS while retaining NP-completness of both coverability and reachability.Comment: 17 pages, 2 figure

On the descriptional complexity of iterative arrays

The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable

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