This paper is a follow-up report to a reading assignment and questionable flaw of the HRU Model and proof of its reachability. A special instance of a Turing machine is considered by a challenge made to the correctness of the original proof. The inspection of this challenge concludes

this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering. 1. Introduction

This paper presents a mereotopological model of polygonal regions of the Euclidean plane and an undecidability proof of its firstorder theory. Restricted to the primitive operations the model is a Boolean algebra. Its single primitive predicate defines simple polygons as the topologically simplest

of F terms and showed that the termination of this procedure is equivalent to the termination of its major component, a procedure for checking the subtype relation between F types. This procedure was thought to terminate on all inputs, but the discovery of a subtle bug in a purported proof

rem Proving and Typechecking The PVS specification language is based on classical, simply typed higher-order logic, but the type system has been augmented with subtypes and dependent types. Though typechecking is undecidable for the PVS type system, the PVS typechecker automatically checks

Here are some brief notes on the classic proof of the undecidability of the Halting Problem. The lecture notes don’t explictly cover the technique of diagonalisation, but it’s an important

We present an undecidability proof of the notion of communication errors in the polyadic #-calculus. The demonstration follows a general pattern of undecidability proofs -- reducing a well-known undecidable problem to the problem in question. We make use of an encoding of the #-calculus

The k-provability problem is, given a first order formula φ and an integer k, to determine if φ has a proof consisting of k or fewer lines (i.e., formulas or sequents). This paper shows that the k-provability problem for the sequent calculus is undecidable. Indeed, for every r

of the universal modality), thereby showing that these problems are undecidable for basic hybrid logics. Recently, unification has been introduced as an important reasoning service for description logics. The undecidability proof for K with nominals can be used to show the undecidability of unification for Boolean

It is shown that it is undecidable in general whether a graph rewriting system (in the "double pushout approach") is terminating. The proof is by a reduction of the Post Correspondence Problem. It is also argued that there is no straightforward reduction of the halting problem