Undecidable problem

About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.

A calculus for shapes in time and space

Abstract: We present a spatial and temporal logic based on Duration Calculus for the specification and verification of mobile real-time systems. We demonstrate the use of the formalism and apply it to a case study. We extend a pure Duration Calculus specification for the controller by spatial assumptions to reason about spatial system properties. We prove that the formalism is undecidable in general for discrete and continuous domains and present a decidable fragment.

A note on undecidable extensions of monadic second order successor arithmetic.

Abstract: Let SC (sequential calculus) be the interpreted system of monadic second order arithmetic with 0, ' as nonlogical constants for zero and successor function and with first order and monadic second order quantifiers. Btichi [1] proved that the theory given by SC is decidable. In this note we show by a generalization of a method presented in Elgot-Rabin [2] that the theory resulting from SC by adjoining a unary function with an infinite inverse image for infinitely many numbers is undecidable (Theorem 1). This serves to prove a conjecture of Siefkes [4] concerning the undecidability of an extended theory SC +h , where h is a unary function of a certain growth (Theorem 2). We adopt the notation of Siefkes [4].

Hereditary History Preserving Bisimilarity Is Undecidable

Abstract: History preserving bisimilarity (hp-bisimilarity) and hereditary history preserving bisimilarity (hhp-bisimilarity) are behavioural equivalences taking into account causal relationships between events of concurrent systems. Their prominent feature is being preserved under action refinement, an operation important for the top-down design of concurrent systems. We show that--unlike hp-bisimilarity--checking hhpbisimilarity for finite labelled asynchronous transition systems is not decidable, by a reduction from the halting problem of 2-counter machines. To make the proof more transparent we introduce an intermediate problem of checking domino bisimilarity for origin constrained tiling systems, whose undecidability is interesting in its own right. We also argue that the undecidability of hhp-bisimilarity holds for finite labelled 1-safe Petri nets.

5' → 3' Watson-Crick Automata with Several Runs.

Abstract: 5′ → 3′ WK-automata are Watson-Crick automata whose two heads start on opposite ends of the input word and always run in opposite directions. One full reading in both directions is called a run. We prove that the expressive power of these automata increases with every additional run that they can make, both for deterministic and non-deterministic machines. This defines two incomparable infinite hierarchies of language classes between the regular and the context-sensitive languages. These hierarchies are complemented with classes defined by several restricted variants of 5′ → 3′ WK-automata like stateless automata. Finally we show that several standard problems are undecidable for languages accepted by 5′ → 3′ WK-automata in only one run, for example the emptiness and the finiteness problems.