arXiv subjects

Alexander A. Rubtsov

Publications and source records attributed to Alexander A. Rubtsov.

3 recordsLinked to original sources

arXiv2017

On computational complexity of Set Automata

We consider a computational model which is known as set automata. The set automata are one-way finite automata with an additional storage---the set. There are two kinds of set automata---the deterministic and the nondeterministic ones. We denote them as DSA and NSA respectively. The model was introduced by M. Kutrib, A. Malcher, M. Wendlandt in 2014. It was shown that DSA-languages look similar to DCFL due to their closure properties and NSA-languages look similar to CFL due to their undecidability properties. In this paper we show that this similarity is natural: we prove that languages recognizable by NSA form a rational cone, so as CFL. The main topic of this paper is computational complexity: we prove that - languages recognizable by DSA belong to P and there are P-complete languages among them; - languages recognizable by NSA are in NP and there are NP-complete languages among them; - the word membership problem is P-complete for DSA without epsilon-loops and PSPACE-complete for general DSA; - the emptiness problem is in PSPACE for NSA and, moreover, it is PSPACE-complete for DSA.

cs.FL↗

arXiv2015

Regular realizability problems and context-free languages

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. In this paper we focus on the case of context-free filters. Algorithmic complexity of the RR problem is a very coarse measure of context-free languages complexity. This characteristic is compatible with rational dominance. We present examples of P-complete RR problems as well as examples of RR problems in the class NL. Also we discuss RR problems with context-free filters that might have intermediate complexity. Possible candidates are the languages with polynomially bounded rational indices.

cs.FL↗

arXiv2015

Regular realizability problems and regular languages

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. We consider two kind of problems depending on representation of regular language. If a regular language on input is represented by a DFA, then we obtain (deterministic) regular realizability problem and we show that in this case the complexity of regular realizability problem for an arbitrary regular filter is either L-complete or NL-complete. We also show that in case of representation regular language on input by NFA the problem is always NL-complete.

cs.FL↗