A recent collection of papers in the last years have given a renovated interest to the notion of orbit decidability. This is a new quite general algorithmic notion, connecting with several classical results, and closely related to the study of the conjugacy problem for extensions of groups. In the present survey we explain several of the classical results closely related to this concept, and we...

A proof of decidability of equivalence between deterministic pushdown automata is presented using a mixture of methods developed in concurrency and language theory. The technique appeals to a tableau proof system for equivalence of configurations of strict deterministic grammars.

It is well-known that the basic modal logic of all topological spaces is S4. However, the structure of basic modal and hybrid logics of classes of spaces satisfying various separation axioms was until present unclear. We prove that modal logics of T0, T1 and T2 topological spaces coincide and are S4. We also examine basic hybrid logics of these classes and prove their decidability; as part of t...

We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decid-ability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separat...

We give resource bounded versions of the Completeness Theorem for propositional and predicate logic. For example, it is well known that every computable consistent propositional theory has a computable complete consistent extension. We show that, when length is measured relative to the binary representation of natural numbers and formulas, every polynomial time decidable propositional theory ha...

Mereology is a theory based on a binary predicate “being a part of.” Most philosophers believe that such a predicate must at least define a partial ordering: that is, it is reflexive (P1), antisymmetric (P2) and transitive (P3). In other words, three basic principles of mereology can thus be fixed. The theory axiomatized by these three basic principles is called ground mereology (GM). There are...