13 research outputs found
Remarks on separating words
The separating words problem asks for the size of the smallest DFA needed to
distinguish between two words of length <= n (by accepting one and rejecting
the other). In this paper we survey what is known and unknown about the
problem, consider some variations, and prove several new results
Using Sat solvers for synchronization issues in partial deterministic automata
We approach the task of computing a carefully synchronizing word of minimum
length for a given partial deterministic automaton, encoding the problem as an
instance of SAT and invoking a SAT solver. Our experimental results demonstrate
that this approach gives satisfactory results for automata with up to 100
states even if very modest computational resources are used.Comment: 15 pages, 3 figure
An equimorphic diversity case
AbstractB.M. Schein has proved that in the semigroup variety NB=Mod(x2=x,xuvy=xvuy) of normal bands one can find at most four pairwise non-isomorphic semigroups with isomorphic monoids of endomorphisms. We prove here the same result for the extension semigroup variety NB˜=Mod(x2y=xy,xuvy=xvuy) of NB, properly separated from NB only by the variety of inflations of the NB-semigroups
Towards parametrizing word equations
Classically, in order to resolve an equation u ≈ v over a free
monoid X*, we reduce it by a suitable family of substitutions
to a family of equations uf ≈ vf, , each involving less
variables than u ≈ v, and then combine solutions of uf ≈ vf
into solutions of u ≈ v. The problem is to get in a handy
parametrized form. The method we propose consists in parametrizing the
path traces in the so called graph of prime equations associated to
u ≈ v. We carry out such a parametrization in the case the prime
equations in the graph involve at most three variables
Looking for pairs that hard to separate: a quantum approach
Determining the minimum number of states required by a deterministic finite automaton to separate a given pair of different words (to accept one word and to reject the other) is an important challenge. In this paper, we ask the same question for quantum finite automata (QFAs). We classify such pairs as easy and hard ones. We show that 2-state QFAs with real amplitudes can separate any easy pair with zero-error but cannot separate some hard pairs even in nondeterministic accepta