Decidability of code properties

Decidability of code properties

We explore the borderline between decidability and undecidability of the following question: “Let C be a class of codes. Given a machineM of type X , is it decidable whether the language L(M) lies in C or not?” for codes in general, ω-codes, codes of finite and bounded deciphering delay, prefix, suffix and bi(pre)fix codes, and for finite automata equipped with different versions of push-down s...

Decidability of Code Properties Henning Fernau and Klaus Reinhardt

Formal Descriptions of Code Properties: Decidability, Complexity, Implementation

The branch of coding theory that is based on formal languages has produced several methods for defining code properties, including word relations, dependence systems, implicational conditions, trajectories, and language inequations. Of those, the latter three can be viewed as formal methods in the sense that a certain formal expression can be used to denote a code property. Here we present a fo...

Decidability Properties of Recursive Types

In this paper we study decision problems and invertibility for two notions of equivalence of recursive types. In particular, for recursive types presented by means of a recursion operator μ, we describe an algorithm showing that the natural equivalence generated by finitely many steps of folding and unfolding of μ-types is decidable. For recursive types presented by finite systems of recursive ...

Decidability properties for fragments of CHR

We study the decidability of termination for two CHR dialects which, similarly to the Datalog like languages, are defined by using a signature which does not allow function symbols (of arity > 0). Both languages allow the use of the = built-in in the body of rules, thus are built on a host language that supports unification. However each imposes one further restriction. The first CHR dialect al...