35 research outputs found
Axiomatizing Flat Iteration
Flat iteration is a variation on the original binary version of the Kleene
star operation P*Q, obtained by restricting the first argument to be a sum of
atomic actions. It generalizes prefix iteration, in which the first argument is
a single action. Complete finite equational axiomatizations are given for five
notions of bisimulation congruence over basic CCS with flat iteration, viz.
strong congruence, branching congruence, eta-congruence, delay congruence and
weak congruence. Such axiomatizations were already known for prefix iteration
and are known not to exist for general iteration. The use of flat iteration has
two main advantages over prefix iteration: 1.The current axiomatizations
generalize to full CCS, whereas the prefix iteration approach does not allow an
elimination theorem for an asynchronous parallel composition operator. 2.The
greater expressiveness of flat iteration allows for much shorter completeness
proofs.
In the setting of prefix iteration, the most convenient way to obtain the
completeness theorems for eta-, delay, and weak congruence was by reduction to
the completeness theorem for branching congruence. In the case of weak
congruence this turned out to be much simpler than the only direct proof found.
In the setting of flat iteration on the other hand, the completeness theorems
for delay and weak (but not eta-) congruence can equally well be obtained by
reduction to the one for strong congruence, without using branching congruence
as an intermediate step. Moreover, the completeness results for prefix
iteration can be retrieved from those for flat iteration, thus obtaining a
second indirect approach for proving completeness for delay and weak congruence
in the setting of prefix iteration.Comment: 15 pages. LaTeX 2.09. Filename: flat.tex.gz. On A4 paper print with:
dvips -t a4 -O -2.15cm,-2.22cm -x 1225 flat. For US letter with: dvips -t
letter -O -0.73in,-1.27in -x 1225 flat. More info at
http://theory.stanford.edu/~rvg/abstracts.html#3
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
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
Equivalence of recursive specifications in process algebra
We define an equivalence relation on recursive specifications in process algebra that is model-independent and does not involve an explicit notion of solution. Then we extend this equivalence to the specification language CRL
A general conservative extension theorem in process algebras with inequalities
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc
On Kleene Algebra vs. Process Algebra
We try to clarify the relationship between Kleene algebra and process
algebra, based on the very recent work on Kleene algebra and process algebra.
Both for concurrent Kleene algebra (CKA) with communications and truly
concurrent process algebra APTC with Kleene star and parallel star, the
extended Milner's expansion law holds, with being primitives (atomic actions),
being the parallel composition, being the alternative composition,
being the sequential composition and the communication merge with the
background of computation. CKA and APTC are all the truly concurrent
computation models, can have the same syntax (primitives and operators), maybe
have the same or different semantics
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