Reactive Turing machines

Abstract

We propose reactive Turing machines (RTMs), extending classical Turing machines with a process-theoretical notion of interaction, and use it to define a notion of executable transition system. We show that every computable transition system with a bounded branching degree is simulated modulo divergence-preserving branching bisimilarity by an RTM, and that every effective transition system is simulated modulo the variant of branching bisimilarity that does not require divergence preservation. We conclude from these results that the parallel composition of (communicating) RTMs can be simulated by a single RTM. We prove that there exist universal RTMs modulo branching bisimilarity, but these essentially employ divergence to be able to simulate an RTM of arbitrary branching degree. We also prove that modulo divergence-preserving branching bisimilarity there are RTMs that are universal up to their own branching degree. We establish a correspondence between executability and finite definability in a simple process calculus. Finally, we establish that RTMs are at least as expressive as persistent Turing machines.

Towards a Coalgebraic Chomsky Hierarchy

“…To this end we will relate tape automata and a special form of Turing machine called reactive Turing machines. Reactive Turing machines were introduced by Baeten et al [43] with the aim to equip TM's with a notion of interaction and so bridge the gap between classical computation and concurrency theory. However, their notion of reactive TM is non-deterministic, and the semantics of reactive TM's is defined in terms of bisimilarity and not in terms of the more classical languages (or traces).…”

Sequential Composition in the Presence of Intermediate Termination (Extended Abstract)

“…If the standard process algebraic specifications of such memory processes are generalised to a setting with intermediate termination, then either they are not always terminating, or they are 'forgetful' and may non-deterministically lose data. This is a concern when one tries to specify the behaviour of a pushdown automaton or a Reactive Turing machine in a process calculus [5,19,20]. The process calculus TCP with iteration and nesting is Turing complete [11,12].…”

Algorithmic Iteration for Computational Intelligence

“…As a consequence, "an ultraintelligent machine could design even better machines", with the result of an intelligence explosion. 5 Since its original account, super-intelligence is formulated on the explicit condition that, in order to improve, the machine must have some understanding of itself. In recent, more technically nuanced analyses, the qualification of an artificial agent which attains super-intelligence through a series of self-improvements is identified with the ability to compare itself with previous systems equipped with progressively higher levels of intelligence, e.g.…”

“…4 See for example [72]. 5 Citations are from [38], considered the first speculation on machine super-intelligence. See [14] for the most up-to-date and complete analysis currently available for the problems, strategies and forecasts related to the possibility of an artificial super-intelligence.…”

“…Even from a purely technical perspective, the precise definition of the computational schema allowed by the notion of algorithm have been seeing a shift in understanding. Most notably, new forms of computation not strictly admitted by the historically qualified notion of mechanical computation by a Turing Machine reflect advancements in the required formal engineering: this is the case, for example, of interactive computing, where Turing Machines have been extended to work with infinite data streams [52]; reactive computing, where interaction in Turing Machines is modelled after concurrency theory [5]; distributed computing, where consistency, availability and partition-tolerance over data are exclusive properties [35,62]. To be able to offer a general argument on algorithms that does not exclude explicitly any of these forms, we will stick to the most abstract definition of the term: we intend an algorithm as a mechanically executable, ordered (possibly non-terminating) list of (multiple, interacting) steps for the application of computable functions on a well-defined domain of input values (be these simple or streams of infinite and complex nature).…”