225 research outputs found
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
Design of asynchronous supervisors
One of the main drawbacks while implementing the interaction between a plant
and a supervisor, synthesised by the supervisory control theory of
\citeauthor{RW:1987}, is the inexact synchronisation. \citeauthor{balemiphdt}
was the first to consider this problem, and the solutions given in his PhD
thesis were in the domain of automata theory. Our goal is to address the issue
of inexact synchronisation in a process algebra setting, because we get
concepts like modularity and abstraction for free, which are useful to further
analyze the synthesised system. In this paper, we propose four methods to check
a closed loop system in an asynchronous setting such that it is branching
bisimilar to the modified (asynchronous) closed loop system. We modify a given
closed loop system by introducing buffers either in the plant models, the
supervisor models, or the output channels of both supervisor and plant models,
or in the input channels of both supervisor and plant models. A notion of
desynchronisable closed loop system is introduced, which is a class of
synchronous closed loop systems such that they are branching bisimilar to their
corresponding asynchronous versions. Finally we study different case studies in
an asynchronous setting and then try to summarise the observations (or
conditions) which will be helpful in order to formulate a theory of
desynchronisable closed loop systems
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
Semantics for PROLOG via term rewrite systems
The authors present semantics for logic programs using term rewrite systems. Reading program lines from left to right (so reversing the arrows), considering the result as a rewrite system, immediately gives the usual declarative semantics (the least Herbrand model). Then the authors add a priority ordering on the rewrite rules, and obtain a procedural semantics for Prolog with depth-first search rule. This gives the authors different semantics in the same settin
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
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 theory
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