L(A)=L(B)? decidability results from complete formal systems

L(A) = L(B)? Decidability Results from Complete Formal Systems

The equivalence problem for deterministic pushdown automata is shown to be decidable. We exhibit a complete formal system for deducing equivalent pairs of deterministic rational boolean series on the alphabet associated with a dpda M. We then extend the result to deterministic pushdown transducers from a free monoid into an abelian group. A general algebraic and logical framework, inspired by H...

Edge Grammars: Decidability Results and Formal Language Issues

A Survey of Decidability Results for Elementary Object Systems

This contribution presents the formalism of Elementary Object Systems (Eos). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. Since object nets in general are immediately Turing complete, we introduce the restricted class of elementary object nets which restrict the nesting of nets to the depth of two. One central aim of this contr...

Decidability Results for Well-Structured Transition Systems with Auxiliary Storage

We consider the problem of verifying the safety of wellstructured transition systems (WSTS) with auxiliary storage. WSTSs with storage are automata that have (possibly) infinitely many control states along with an auxiliary store, but which have a well-quasi-ordering on the set of control states. The set of reachable configurations of the automaton may themselves not be well-quasi-ordered becau...

A Survey of Elementary Object Systems Part I: Decidability Results

This contribution presents the formalism of Elementary Object Systems (Eos). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. Since object nets in general are immediately Turing complete, we introduce the restricted class of elementary object nets which restrict the nesting of nets to the depth of two. In this work we study the rel...