Related papers: The Recursion Theorem from a Different Angle
The main deficiency of the algorithms running on digital computers nowadays is their inability to change themselves during the execution. In line with this, the paper introduces the so-called replicated algorithms, inspired by the concept…
In 2005, Rampersad and the second author proved a number of theorems about infinite words x with the property that if w is any sufficiently long finite factor of x, then its reversal w^R is not a factor of x. In this note we revisit these…
Recoverable algorithms tolerate failures and recoveries of processes by using non-volatile memory. Of particular interest are self-implementations of key operations, in which a recoverable operation is implemented from its non-recoverable…
This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Caminada,…
While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…
Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are…
Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the…
Termination is a central property in sequential programming models: a term is terminating if all its reduction sequences are finite. Termination is also important in concurrency in general, and for message-passing programs in particular. A…
We present a heuristic framework for attacking the undecidable termination problem of logic programs, as an alternative to current termination/non-termination proof approaches. We introduce an idea of termination prediction, which predicts…
Consider a decision problem whose instance is a function. Its degree of undecidability, measured by the corresponding class of the arithmetic (or Kleene-Mostowski) hierarchy hierarchy, may depend on whether the instance is a partial…
An uninterpreted program (UP) is a program whose semantics is defined over the theory of uninterpreted functions. This is a common abstraction used in equivalence checking, compiler optimization, and program verification. While simple, the…
Mitchison and Jozsa recently suggested that the "chained-Zeno" counterfactual computation protocol recently proposed by Hosten et al. is counterfactual for only one output of the computer. This claim was based on the existing abstract…
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
In a reversible language, any forward computation can be undone by a finite sequence of backward steps. Reversible computing has been studied in the context of different programming languages and formalisms, where it has been used for…
The paper considers the halting scheme for quantum Turing machines. The scheme originally proposed by Deutsch appears to be correct, but not exactly as originally intended. We discuss the result of Ozawa as well as the objections raised by…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…
Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the behaviours produced by them under execution, the interaction…
In contrast to software reverse engineering, there are hardly any tools available that support hardware reversing. Therefore, the reversing process is conducted by human analysts combining several complex semi-automated steps. However,…
In modern computers, computation is performed by assembling together sets of logic gates. Popular gates like AND, OR, XOR, processing two logic inputs and yielding one logic output, are often addressed as irreversible logic gates where the…
Recent investigations into the physical nature of information and fundamental limits to information transmission have revealed questions such as the possibility of superluminal data transfer or not; and whether reversible computation…