9,057 research outputs found
Reactive Turing Machines
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. Finally, we establish a correspondence
between executability and finite definability in a simple process calculus
Reactive Turing machines
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
Reactive Turing machines
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
The -Calculus is Behaviourally Complete and Orbit-Finitely Executable
Reactive Turing machines extend classical Turing machines with a facility to
model observable interactive behaviour. We call a behaviour (finitely)
executable if, and only if, it is equivalent to the behaviour of a (finite)
reactive Turing machine. In this paper, we study the relationship between
executable behaviour and behaviour that can be specified in the -calculus.
We establish that every finitely executable behaviour can be specified in the
-calculus up to divergence-preserving branching bisimilarity. The
converse, however, is not true due to (intended) limitations of the model of
reactive Turing machines. That is, the -calculus allows the specification
of behaviour that is not finitely executable up to divergence-preserving
branching bisimilarity. We shall prove, however, that if the finiteness
requirement on reactive Turing machines and the associated notion of
executability is relaxed to orbit-finiteness, then the -calculus is
executable up to (divergence-insensitive) branching bisimilarity.Comment: arXiv admin note: text overlap with arXiv:1508.0485
On the Executability of Interactive Computation
The model of interactive Turing machines (ITMs) has been proposed to
characterise which stream translations are interactively computable; the model
of reactive Turing machines (RTMs) has been proposed to characterise which
behaviours are reactively executable. In this article we provide a comparison
of the two models. We show, on the one hand, that the behaviour exhibited by
ITMs is reactively executable, and, on the other hand, that the stream
translations naturally associated with RTMs are interactively computable. We
conclude from these results that the theory of reactive executability subsumes
the theory of interactive computability. Inspired by the existing model of ITMs
with advice, which provides a model of evolving computation, we also consider
RTMs with advice and we establish that a facility of advice considerably
upgrades the behavioural expressiveness of RTMs: every countable transition
system can be simulated by some RTM with advice up to a fine notion of
behavioural equivalence.Comment: 15 pages, 0 figure
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
Towards a Uniform Theory of Effectful State Machines
Using recent developments in coalgebraic and monad-based semantics, we
present a uniform study of various notions of machines, e.g. finite state
machines, multi-stack machines, Turing machines, valence automata, and weighted
automata. They are instances of Jacobs' notion of a T-automaton, where T is a
monad. We show that the generic language semantics for T-automata correctly
instantiates the usual language semantics for a number of known classes of
machines/languages, including regular, context-free, recursively-enumerable and
various subclasses of context free languages (e.g. deterministic and real-time
ones). Moreover, our approach provides new generic techniques for studying the
expressivity power of various machine-based models.Comment: final version accepted by TOC
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