An Intensional Concurrent Faithful Encoding of Turing Machines

The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to support arbitrary computation. However, these encodings are usually by simulating the entire Turing Machine within the language, or by encoding a language that does an encoding or simulation itself. This second category is typical for process calculi that show an encoding of lambda-calculus (often with restrictions) that in turn simulates a Turing Machine. Such approaches lead to indirect encodings of Turing Machines that are complex, unclear, and only weakly equivalent after computation. This paper presents an approach to encoding Turing Machines into intensional process calculi that is faithful, reduction preserving, and structurally equivalent. The encoding is demonstrated in a simple asymmetric concurrent pattern calculus before generalised to simplify infinite terms, and to show encodings into Concurrent Pattern Calculus and Psi Calculi.Comment: In Proceedings ICE 2014, arXiv:1410.701

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 allows only range-restricted rules, that is, it does not allow the use of variables in the body or in the guard of a rule if they do not appear in the head. We show that the existence of an infinite computation is decidable for this dialect. The second dialect instead limits the number of atoms in the head of rules to one. We prove that in this case, the existence of a terminating computation is decidable. These results show that both dialects are strictly less expressive than Turing Machines. It is worth noting that the language (without function symbols) without these restrictions is as expressive as Turing Machines

Characterizing traits of coordination

How can one recognize coordination languages and technologies? As this report shows, the common approach that contrasts coordination with computation is intellectually unsound: depending on the selected understanding of the word "computation", it either captures too many or too few programming languages. Instead, we argue for objective criteria that can be used to evaluate how well programming technologies offer coordination services. Of the various criteria commonly used in this community, we are able to isolate three that are strongly characterizing: black-box componentization, which we had identified previously, but also interface extensibility and customizability of run-time optimization goals. These criteria are well matched by Intel's Concurrent Collections and AstraKahn, and also by OpenCL, POSIX and VMWare ESX.Comment: 11 pages, 3 table

A Foundation of Programming a Multi-Tape Quantum Turing machine

The notion of quantum Turing machines is a basis of quantum complexity theory. We discuss a general model of multi-tape, multi-head Quantum Turing machines with multi final states that also allow tape heads to stay still.Comment: A twelve page version is to appear in the Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science in September, 1999. LNC

On the Expressive Power of Multiple Heads in CHR

Constraint Handling Rules (CHR) is a committed-choice declarative language which has been originally designed for writing constraint solvers and which is nowadays a general purpose language. CHR programs consist of multi-headed guarded rules which allow to rewrite constraints into simpler ones until a solved form is reached. Many empirical evidences suggest that multiple heads augment the expressive power of the language, however no formal result in this direction has been proved, so far. In the first part of this paper we analyze the Turing completeness of CHR with respect to the underneath constraint theory. We prove that if the constraint theory is powerful enough then restricting to single head rules does not affect the Turing completeness of the language. On the other hand, differently from the case of the multi-headed language, the single head CHR language is not Turing powerful when the underlying signature (for the constraint theory) does not contain function symbols. In the second part we prove that, no matter which constraint theory is considered, under some reasonable assumptions it is not possible to encode the CHR language (with multi-headed rules) into a single headed language while preserving the semantics of the programs. We also show that, under some stronger assumptions, considering an increasing number of atoms in the head of a rule augments the expressive power of the language. These results provide a formal proof for the claim that multiple heads augment the expressive power of the CHR language.Comment: v.6 Minor changes, new formulation of definitions, changed some details in the proof

Is there any real substance to the claims for a 'new computationalism'?

'Computationalism' is a relatively vague term used to describe attempts to apply Turing's model of computation to phenomena outside its original purview: in modelling the human mind, in physics, mathematics, etc. Early versions of computationalism faced strong objections from many (and varied) quarters, from philosophers to practitioners of the aforementioned disciplines. Here we will not address the fundamental question of whether computational models are appropriate for describing some or all of the wide range of processes that they have been applied to, but will focus instead on whether `renovated' versions of the \textit{new computationalism} shed any new light on or resolve previous tensions between proponents and skeptics. We find this, however, not to be the case, because the 'new computationalism' falls short by using limited versions of "traditional computation", or proposing computational models that easily fall within the scope of Turing's original model, or else proffering versions of hypercomputation with its many pitfalls