Solving word equations

Solving Word Equations modulo Partial Commutations

The Hardness of Solving Simple Word Equations

We investigate the class of regular-ordered word equations. The sides of such an equation contain both exactly the same variables, occurring in the same order (but separated by potentially distinct constant factors). Surprisingly, we obtain that solving even such simple equations is NP-hard. By considerations regarding the combinatorial structure of the minimal solutions of the more general qua...

Solving Word Jumbles

Debabrata Sengupta, Abhishek Sharma {dsgupta, abhisheksharma} @ stanford.edu Solving Word Jumbles We propose to develop an android based application that can assist the user in solving word jumbles commonly found in newspapers and magazines. An example of a typical word jumble which might be found in a book of puzzles is shown in the figure below. Goals : We envisage that the application should...

Solving Bit-Vector Equations

This paper is concerned with solving equations on xed and non-xed size bit-vector terms. We deene an equational transformation system for solving equations on terms where all sizes of bit-vectors and extraction positions are known. This transformation system suggests a generalization for dealing with bit-vectors of unknown size and unknown extraction positions. Both solvers adhere to the princi...

Solving Pseudo-Differential Equations

In 1957, Hans Lewy constructed a counterexample showing that very simple and natural differential equations can fail to have local solutions. A geometric interpretation and a generalization of this counterexample were given in 1960 by L.Hörmander. In the early seventies, L.Nirenberg and F.Treves proposed a geometric condition on the principal symbol, the so-called condition (ψ), and provided st...