211 research outputs found
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
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
Sequential Composition in the Presence of Intermediate Termination (Extended Abstract)
The standard operational semantics of the sequential composition operator
gives rise to unbounded branching and forgetfulness when transparent process
expressions are put in sequence. Due to transparency, the correspondence
between context-free and pushdown processes fails modulo bisimilarity, and it
is not clear how to specify an always terminating half counter. We propose a
revised operational semantics for the sequential composition operator in the
context of intermediate termination. With the revised operational semantics, we
eliminate transparency, allowing us to establish a close correspondence between
context-free processes and pushdown processes. Moreover, we prove the reactive
Turing powerfulness of TCP with iteration and nesting with the revised
operational semantics for sequential composition.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.00049. arXiv admin note:
substantial text overlap with arXiv:1706.0840
Sequential Composition in the Presence of Intermediate Termination (Extended Abstract)
The standard operational semantics of the sequential composition operator gives rise to unbounded branching and forgetfulness when transparent process expressions are put in sequence. Due to transparency, the correspondence between context-free and pushdown processes fails modulo bisimilarity, and it is not clear how to specify an always terminating half counter. We propose a revised operational semantics for the sequential composition operator in the context of intermediate termination. With the revised operational semantics, we eliminate transparency, allowing us to establish a close correspondence between context-free processes and pushdown processes. Moreover,we prove the reactive Turing powerfulness of TCP with iteration and nesting with the revised operational semantics for sequential composition
Parallel Pushdown Automata and Commutative Context-Free Grammars in Bisimulation Semantics (Extended Abstract)
A classical theorem states that the set of languages given by a pushdown
automaton coincides with the set of languages given by a context-free grammar.
In previous work, we proved the pendant of this theorem in a setting with
interaction: the set of processes given by a pushdown automaton coincides with
the set of processes given by a finite guarded recursive specification over a
process algebra with actions, choice, sequencing and guarded recursion, if and
only if we add sequential value passing. In this paper, we look what happens if
we consider parallel pushdown automata instead of pushdown automata, and a
process algebra with parallelism instead of sequencing.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.05788. arXiv admin note:
text overlap with arXiv:2203.0171
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
Parallel Pushdown Automata and Commutative Context-Free Grammars in Bisimulation Semantics
A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction: the set of processes given by a pushdown automaton coincides with the set of processes given by a finite guarded recursive specification over a process algebra with actions, choice, sequencing and guarded recursion, if and only if we add sequential value passing. In this paper, we look what happens if we consider parallel pushdown automata instead of pushdown automata, and a process algebra with parallelism instead of sequencing.</p
From computability to executability : a process-theoretic view on automata theory
The theory of automata and formal language was devised in the 1930s to provide models for and to reason about computation. Here we mean by computation a procedure that transforms input into output, which was the sole mode of operation of computers at the time. Nowadays, computers are systems that interact with us and also each other; they are non-deterministic, reactive systems. Concurrency theory, split off from classical automata theory a few decades ago, provides a model of computation similar to the model given by the theory of automata and formal language, but focuses on concurrent, reactive and interactive systems. This thesis investigates the integration of the two theories, exposing the differences and similarities between them. Where automata and formal language theory focuses on computations and languages, concurrency theory focuses on behaviour. To achieve integration, we look for process-theoretic analogies of classic results from automata theory. The most prominent difference is that we use an interpretation of automata as labelled transition systems modulo (divergence-preserving) branching bisimilarity instead of treating automata as language acceptors. We also consider similarities such as grammars as recursive specifications and finite automata as labelled finite transition systems. We investigate whether the classical results still hold and, if not, what extra conditions are sufficient to make them hold. We especially look into three levels of Chomsky's hierarchy: we study the notions of finite-state systems, pushdown systems, and computable systems. Additionally we investigate the notion of parallel pushdown systems. For each class we define the central notion of automaton and its behaviour by associating a transition system with it. Then we introduce a suitable specification language and investigate the correspondence with the respective automaton (via its associated transition system). Because we not only want to study interaction with the environment, but also the interaction within the automaton, we make it explicit by means of communicating parallel components: one component representing the finite control of the automaton and one component representing the memory. First, we study finite-state systems by reinvestigating the relation between finite-state automata, left- and right-linear grammars, and regular expressions, but now up to (divergence-preserving) branching bisimilarity. For pushdown systems we augment the finite-state systems with stack memory to obtain the pushdown automata and consider different termination styles: termination on empty stack, on final state, and on final state and empty stack. Unlike for language equivalence, up to (divergence-preserving) branching bisimilarity the associated transition systems for the different termination styles fall into different classes. We obtain (under some restrictions) the correspondence between context-free grammars and pushdown automata for termination on final state and empty stack. We show how for contrasimulation, a weaker equivalence than branching bisimilarity, we can obtain the correspondence result without some of the restrictions. Finally, we make the interaction within a pushdown automaton explicit, but in a different way depending on the termination style. By analogy of pushdown systems we investigate the parallel pushdown systems, obtained by augmenting finite-state systems with bag memory, and consider analogous termination styles. We investigate the correspondence between context-free grammars that use parallel composition instead of sequential composition and parallel pushdown automata. While the correspondence itself is rather tight, it unfortunately only covers a small subset of the parallel pushdown automata, i.e. the single-state parallel pushdown automata. When making the interaction within parallel pushdown automata explicit, we obtain a rather uniform result for all termination styles. Finally, we study computable systems and the relation with exective and computable transition systems and Turing machines. For this we present the reactive Turing machine, a classical Turing machine augmented with capabilities for interaction. Again, we make the interaction in the reactive Turing machine between its finite control and the tape memory explicit
Sequencing and intermediate acceptance: Axiomatisation and decidability of bisimilarity
The Theory of Sequential Processes includes deadlock, successful termination, action prefixing, alternative and sequential composition. Intermediate acceptance, which is important for the integration of classical automata theory, can be expressed through a combination of alternative composition and successful termination. Recently, it was argued that complications arising from the interplay between intermediate acceptance and sequential composition can be eliminated by replacing sequential composition by sequencing. In this paper we study the equational theory of the recursion-free fragment of the resulting process theory modulo bisimilarity, proving that it is not finitely based, but does afford a ground-complete axiomatisation if a unary auxiliary operator is added. Furthermore, we prove that bisimilarity is decidable for processes definable by means of a finite guarded recursive specification over the process the
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