Decidability results for primitive recursive algorithms

Primitive Recursive Decidability for Large Rings of Algebraic Integers

A Representation Theorem for Primitive Recursive Algorithms

We formalize the algorithms computing primitive recursive (PR) functions as the abstract state machines (ASMs) whose running length is computable by a PR function. Then we show that there exists a programming language (implementing only PR functions) by which it is possible to implement any one of the previously defined algorithms for the PR functions in such a way that their complexity is pres...

On primitive recursive algorithms and the greatest common divisor function

We establish linear lower bounds for the complexity of non-trivial, primitive recursive algorithms from piecewise linear given functions. The main corollary is that logtime algorithms for the greatest common divisor from such givens (such as Stein’s) cannot be matched in efficiency by primitive recursive algorithms from the same given functions. The question is left open for the Euclidean algor...

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 ...

Non-primitive recursive decidability of products of modal logics with expanding domains

We show that—unlike products of ‘transitive’ modal logics which are usually undecidable— their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component—call it the ‘flow of time’—is • a finite...