COMPUTATIONAL COMPLEXITY OF TERM-EQUIVALENCE

Computational Complexity of Term-Equivalence

Two algebraic structures with the same universe are called term-equivalent if they have the same clone of term operations. We show that the problem of determining whether two finite algebras of finite similarity type are term-equivalent is complete for deterministic exponential time. When are two algebraic structures (presumably of different similarity types) considered to be “the same”, for al...

Computational Complexity of Some Equivalence-Checking Problems

This habilitation thesis gives an overview of five papers of the author in the area of verification, in particular, in the study of computational complexity of equivalence checking problems and related areas. The first of these papers, Sawa, Jančar: Equivalences on Finite-State Systems are PTIME-hard (2005), shows that deciding any relation between bisimulation equivalence (bisimilarity) and tr...

Logical Definability Versus Computational Complexity: Another Equivalence

Logical Deenability versus Computational Complexity: Another Equivalence

We examine two diierent classes of program schemes involving arrays, one class, NPSA(1), allowing arrays in their full generality and the other, NPSB(1), only allowing arrays in a (syntactically) restricted form. Our main result is that the open question of whether the complexity class PSPACE is equal to the complexity class NP is equivalent to whether the class of problems (accepted by the pro...

On the Computational Complexity of the Domination Game

The domination game is played on an arbitrary graph $G$ by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer $k$ is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph $G$ in $mathcal O(Delta(G)cdot |V(G)|^k)$ time. In the special case when $k=3$ and the...