43 research outputs found
On Solving Word Equations Using SAT
We present Woorpje, a string solver for bounded word equations (i.e.,
equations where the length of each variable is upper bounded by a given
integer). Our algorithm works by reformulating the satisfiability of bounded
word equations as a reachability problem for nondeterministic finite automata,
and then carefully encoding this as a propositional satisfiability problem,
which we then solve using the well-known Glucose SAT-solver. This approach has
the advantage of allowing for the natural inclusion of additional linear length
constraints. Our solver obtains reliable and competitive results and,
remarkably, discovered several cases where state-of-the-art solvers exhibit a
faulty behaviour
Surface properties changing of biodegradable polymers by the radio frequency magnetron sputtering modification
Functions for the General Solution of Parametric Word Equations
: In this article we introduce the functions Fi (x 1 , x 2 ) l1,..., ls and Th (x 1 , x 2 , x 3 ) i l1,..., l2s (i = 1, 2, 3), of the word variables x i and of the natural number variables li, where s ³ 0. By means of these functions, we give exactly the general solution (i.e. the set of all the solutions) of the first basic parametric equation: x 1 x 2 x 3 x 4 = x 3 x 1 l x 2 x 5 , in a free monoid. 1. Introduction The following four parametric equations: x 1 x 2 x 3 x 4 = x 3 x 1 l x 2 x 5 , x 1 x 2 x 3 x 4 = x 2 x 3 l x 1 x 5 , x 1 x 2 2 x 3 x 4 = x 3 x 1 2 x 2 x 5 , x 1 x 2 l+1 x 3 x 4 = x 3 x 2 µ+1 x 1 x 5 , in a free monoid, are called basic equations. They arise in the graph of the prefixeequations in free monoid (cf. [2], [3]) and play an important role in the hierarchy of the parametric equations, in reason of the structures of their solutions. In particular, the general solution of any equation in a free monoid of the form F(x 1 , x 2 , x 3 ) x 4 = Y(x 1 , x 2 , ..
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
Solvability of Equations in Free Partially Commutative Groups Is Decidable
Trace monoids are well-studied objects in computer science where they serve as a basic algebraic tool for analyzing concurrent systems