We study a generalization of strongly regular graphs. We call a graph strongly walkregular if there is an ` > 1 such that the number of walks of length ` from a vertex to another vertex depends only on whether the two vertices are the same, adjacent, or not adjacent. We will show that a strongly walk-regular graph must be an empty graph, a complete graph, a strongly regular graph, a disjoint un...

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for c...

Minimization of nondeterministic finite automata (NFA) is a hard problem (PSPACE-complete). Bisimulations are then an attractive alternative for reducing the size of NFAs, as even bisimilarity (the largest bisimulation) is almost linear using the Paige and Tarjan algorithm. NFAs obtained from regular expressions (REs) can have the number of states linear with respect to the size of the REs and ...

In this paper, we show that given a weighted, directed planar graph G, and any > 0, there exists a polynomial time and O(n 1 2+ ) space algorithm that computes the shortest path between two fixed vertices in G. We also consider the RedBluePath problem, which states that given a graph G whose edges are colored either red or blue and two fixed vertices s and t in G, is there a path from s to t in...

The hairpin completion is a natural operation on formal languages which has been inspired by molecular phenomena in biology and by DNAcomputing. In 2009 we presented in [6] a (polynomial time) decision algorithm to decide regularity of the hairpin completion. In this paper we provide four new results: 1.) We show that the decision problem is NL-complete. 2.) There is a polynomial time decision ...

We close the gap in complexity classification of the subsumption problem in the simple description logic FL0, which allows for conjunctions and universal value restriction only. We prove that subsumption in FL0 is PSPACE-complete when cyclic definitions with descriptive semantics are allowed. Our proof uses automata theory and as a by-product the PSPACE-completeness of a certain decision proble...

The stateless deterministic ordered restarting automata accept exactly the regular languages, and it is known that the trade-off for turning a stateless deterministic ordered restarting automaton into an equivalent DFA is at least double exponential. Here we present a construction that yields an equivalent NFA of size 2 from a stateless deterministic ordered restarting automaton that works on a...

Determining for a given deterministic complete automaton the sequence of visited states while reading a given word is the core of important problems with automata-based solutions, such as approximate string matching. The main di3culty is to do this computation e3ciently. Considering words as vectors and working on them using vectorial operations allows to solve the problem faster than using loc...