Solving word equations modulo partial commutations

Solving Word Equations modulo Partial Commutations

Contextual partial commutations

We consider the monoid T with the presentation 〈a, b; aab = aba〉 which is “close” to trace monoids. We prove two different types of results. First, we give a combinatorial description of the lexicographically minimum and maximum representatives of their congruence classes in the free monoid {a, b}∗ and solve the classical equations, such as commutation and conjugacy in T. Then we study the clos...

Solving Linear Equations Modulo Unknown Divisors: Revisited

We revisit the problem of finding small solutions to a collection of linear equations modulo an unknown divisor p for a known composite integer N . In CaLC 2001, Howgrave-Graham introduced an efficient algorithm for solving univariate linear equations; since then, two forms of multivariate generalizations have been considered in the context of cryptanalysis: modular multivariate linear equation...

Regular languages and partial commutations

The closure of a regular language under a [partial] commutation I has been extensively studied. We present new advances on two problems of this area: (1) When is the closure of a regular language under [partial] commutation still regular? (2) Are there any robust classes of languages closed under [partial] commutation? We show that the class Pol(G) of polynomials of group languages is closed un...

Finite difference method for solving partial integro-differential equations

In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...