35 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
The free process algebra generated by δ, ϵ and τ
AbstractWe establish the structure of the initial process algebra with additive and multiplicative identity elements and no article silent step
Process algebra with conditionals in the presence of epsilon
In a previous paper, we presented several extensions of ACP with conditional
expressions, including one with a retrospection operator on conditions to allow
for looking back on conditions under which preceding actions have been
performed. In this paper, we add a constant for a process that is only capable
of terminating successfully to those extensions of ACP, which can be very
useful in applications. It happens that in all cases the addition of this
constant is unproblematic.Comment: 41 page
Another look at abstraction in process algebra: Extended abstract
Central to theories of concurrency is the notion of abstraction. Abstraction from internal actions is the most important tool for system verification. In this paper, we look at abstraction in the framework of the Algebra of Communicating Processes (see BERGSTRA & KLOP [4, 6]). We introduce a hidden step η, and construct a model for the resulting theory ACPη. We briefly look at recursive specifications in this theory, and discuss the relations with Milner's silent step τ
Another look at abstraction in process algebra: Extended abstract
Central to theories of concurrency is the notion of abstraction. Abstraction from internal actions is the most important tool for system verification. In this paper, we look at abstraction in the framework of the Algebra of Communicating Processes (see BERGSTRA & KLOP [4, 6]). We introduce a hidden step η, and construct a model for the resulting theory ACPη. We briefly look at recursive specifications in this theory, and discuss the relations with Milner's silent step τ
A process calculus with finitary comprehended terms
We introduce the notion of an ACP process algebra and the notion of a meadow
enriched ACP process algebra. The former notion originates from the models of
the axiom system ACP. The latter notion is a simple generalization of the
former notion to processes in which data are involved, the mathematical
structure of data being a meadow. Moreover, for all associative operators from
the signature of meadow enriched ACP process algebras that are not of an
auxiliary nature, we introduce variable-binding operators as generalizations.
These variable-binding operators, which give rise to comprehended terms, have
the property that they can always be eliminated. Thus, we obtain a process
calculus whose terms can be interpreted in all meadow enriched ACP process
algebras. Use of the variable-binding operators can have a major impact on the
size of terms.Comment: 25 pages, combined with arXiv:0901.3012 [math.RA]; presentation
improved, mistakes in Table 5 correcte