253 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
Computations and interaction
We enhance the notion of a computation of the classical theory of computing with the notion of interaction. In this way, we enhance a Turing machine as a model of computation to a Reactive Turing Machine that is an abstract model of a computer as it is used nowadays, always interacting with the user and the world
Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract)
The languages accepted by finite automata are precisely the languages denoted
by regular expressions. In contrast, finite automata may exhibit behaviours
that cannot be described by regular expressions up to bisimilarity. In this
paper, we consider extensions of the theory of regular expressions with various
forms of parallel composition and study the effect on expressiveness. First we
prove that adding pure interleaving to the theory of regular expressions
strictly increases its expressiveness up to bisimilarity. Then, we prove that
replacing the operation for pure interleaving by ACP-style parallel composition
gives a further increase in expressiveness. Finally, we prove that the theory
of regular expressions with ACP-style parallel composition and encapsulation is
expressive enough to express all finite automata up to bisimilarity. Our
results extend the expressiveness results obtained by Bergstra, Bethke and
Ponse for process algebras with (the binary variant of) Kleene's star
operation.Comment: In Proceedings EXPRESS'10, arXiv:1011.601
Identification of robust and disease-specific stromal alterations in spondyloarthritis synovitis
IL-17 producing mast cells contribute to synovial inflammation in non-psoriatic and psoriatic spondyloarthritis
Expressiveness modulo bisimilarity of regular expressions with parallel composition
The languages accepted by finite automata are precisely the languages denoted by regular
expressions. In contrast, finite automata may exhibit behaviours that cannot be described by
regular expressions up to bisimilarity. In this paper, we consider extensions of the theory of
regular expressions with various forms of parallel composition and study the effect on
expressiveness. First we prove that adding pure interleaving to the theory of regular
expressions strictly increases its expressiveness modulo bisimilarity. Then, we prove that
replacing the operation for pure interleaving by ACP-style parallel composition gives a
further increase in expressiveness, still insufficient, however, to facilitate the expression of all
finite automata up to bisimilarity. Finally, we prove that the theory of regular expressions
with ACP-style parallel composition and encapsulation is expressive enough to express all
finite automata up to bisimilarity. Our results extend the expressiveness results obtained by
Bergstra, Bethke and Ponse for process algebras with (the binary variant of) Kleene’s star
operation
- …