We investigate bisimulation equivalence on Petri nets under durational semantics. Our motivation was to verify the conjecture that in durational setting, the bisimulation equivalence checking problem becomes more tractable (which is the case, e.g., over communication-free nets). We disprove this conjecture in three of four proposed variants of durational semantics. The fourth case remains an in...

General-valued constraint satisfaction problems (VCSPs) are generalisations of CSPs dealing with homomorphisms between two valued structures. We study the complexity of structural restrictions for VCSPs, that is, restrictions defined by classes of admissible lefthand side valued structures. As our main result, we show that for VCSPs of bounded arity the only tractable structural restrictions ar...

The authors have shown in Courcelle et al. (1982) that certain attribute systems called strongly noneireular can be translated into recursive program schemes taking derivation trees as arguments and called primitive reeursive schemes with parameters. In particular, the equivalence problem for strongly noncircular attribute systems reduces to the equivalence problem for the latter class of progr...

In this paper, we prove that the Hurwitz equivalence problem for 1-factorizations in F2⊕F2 is undecidable, and as a consequence, the Hurwitz equivalence problem for ∆-factorizations in the braid groups Bn, n ≥ 5 is also undecidable.

This article is dedicated to the centenary of the local CR equivalence problem, formulated by Henri Poincaré in 1907. The first part gives an account of Poincaré’s heuristic counting arguments, suggesting existence of infinitely many local CR invariants. Then we sketch the beautiful completion of Poincaré’s approach to the problem in the work of Chern and Moser on Levi nondegenerate hypersurfac...

The equivalence of processes is an important constituent of process optimization. The article considers the functional equivalence problem for processes in object-oriented environments for the case when the turn of executing operations for different objects is not essential. It is shown that this problem can be reduced to the equivalence problem of regular expressions over a partially commutati...

We investigate the computational complexity of deciding whether or not a given polynomial , presented as the sum of monomials, is identically 0 over a ring. It is proved that if the factor by the Jacobson-radical is not commutative, then the problem is coNP-complete.

We investigate which computable equivalence structures are isomorphic relative to the Halting problem.

The notion of succession rule (system for short) provides a powerful tool for the enumeration of many classes of combinatorial objects. Often, different systems exist for a given class of combinatorial objects, and a number of problems arise naturally. An important one is the equivalence problem between two different systems. In this paper, we show how to solve this problem in the case of syste...

Using a result of B.H. Neumann we extend Eilenberg’s Equality Theorem to a general result which implies that the multiplicity equivalence problem of two (nondeterministic) multitape finite automata is decidable. As a corollary we solve a long standing open problem in automata theory, namely, the equivalence problem for multitape deterministic finite automata. The main theorem states that there ...