We study the problem DFA-SW of determining if a given deterministic finite automaton A possesses synchronizing word length at most k for automata whose (multi-)graphs are TTSPL, i.e. , series-parallel, plus allowing some self-loops. While remains NP-complete on TTSPL automata, we also find (further) restrictions with efficient (parameterized) algorithms. complexity related problems, instance, e...

Inapproximability results concerning minimization of nondeterministic finite automata relative to given deterministic finite automata were obtained only recently, modulo cryptographic assumptions [4]. Here we give upper and lower bounds on the approximability of this problem utilizing only the common assumption P 6= NP, in the setup where the input is a finite language specified by a truth tabl...

Planar automata seems to be representative of the synchronizing behavior of deterministic finite state automata. We conjecture that Černy’s conjecture holds true, if and only if, it holds true for planar automata. In this paper we have gathered some evidence concerning this conjecture. This evidence amounts to show that the class of planar automata is representative of the algorithmic hardness ...

Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. We start with the unranked tree automata (UTAs) that are standard in database theory, assuming bottomup determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal UTAs in that class are n...

Modern programming languages use regular expressions to define valid tokens. Traditional lexical analyzers based on minimum deterministic finite automata for regular expressions cannot handle the look-ahead problem. The scanner writer needs to explicitly identify the look-ahead states and code the buffering and re-scanning operations by hand. We identify the class of finite look-ahead finite au...

In this paper we investigate the complexity of planarity of knot diagrams encoded by Gauss words, both in terms of recognition by automata over infinite alphabets and in terms of classical logarithmic space complexity. As the main result, we show that recognition of planarity of unsigned Gauss words can be done in deterministic logarithmic space and by deterministic register automata. We also d...

Quantum finite automata, as well as quantum pushdown automata were first introduced by C. Moore, J. P. Crutchfield [MC 97]. In this paper we introduce the notion of quantum pushdown automata in a non-equivalent way, including unitarity criteria, by using the definition of quantum finite automata of [KW 97]. It is established that the unitarity criteria of quantum pushdown automata are not equiv...