13 research outputs found
Ntyft/ntyxt rules reduce to ntree rules
Groote and Vaandrager introduced the tyft/tyxt format for Transition System Specifications (TSSs), and established that for each TSS in this format that is well-founded, the bisimulation equivalence it induces is a congruence. In this paper, we construct for each TSS in tyft/tyxt format an equivalent TSS that consists of tree rules only. As a corollary we can give an affirmative answer to an open question, namely whether the well-foundedness condition in the congruence theorem for tyft/tyxt can be dropped. These results extend to tyft/tyxt with negative premises and predicates
On the Meaning of Transition System Specifications
Transition System Specifications provide programming and specification
languages with a semantics. They provide the meaning of a closed term as a
process graph: a state in a labelled transition system. At the same time they
provide the meaning of an n-ary operator, or more generally an open term with n
free variables, as an n-ary operation on process graphs. The classical way of
doing this, the closed-term semantics, reduces the meaning of an open term to
the meaning of its closed instantiations. It makes the meaning of an operator
dependent on the context in which it is employed. Here I propose an alternative
process graph semantics of TSSs that does not suffer from this drawback.
Semantic equivalences on process graphs can be lifted to open terms conform
either the closed-term or the process graph semantics. For pure TSSs the latter
is more discriminating. I consider five sanity requirements on the semantics of
programming and specification languages equipped with a recursion construct:
compositionality, applied to n-ary operators, recursion and variables,
invariance under -conversion, and the recursive definition principle,
saying that the meaning of a recursive call should be a solution of the
corresponding recursion equations. I establish that the satisfaction of four of
these requirements under the closed-term semantics of a TSS implies their
satisfaction under the process graph semantics.Comment: In Proceedings EXPRESS/SOS 2019, arXiv:1908.0821
Precongruence Formats with Lookahead through Modal Decomposition
Bloom, Fokkink & van Glabbeek (2004) presented a method to decompose formulas from Hennessy-Milner logic with regard to a structural operational semantics specification. A term in the corresponding process algebra satisfies a Hennessy-Milner formula if and only if its subterms satisfy certain formulas, obtained by decomposing the original formula. They used this decomposition method to derive congruence formats in the realm of structural operational semantics. In this paper it is shown how this framework can be extended to specifications that include bounded lookahead in their premises. This extension is used in the derivation of a congruence format for the partial trace preorder
Abstract Congruence Criteria for Weak Bisimilarity
We introduce three general compositionality criteria over operational
semantics and prove that, when all three are satisfied together, they guarantee
weak bisimulation being a congruence. Our work is founded upon Turi and
Plotkin's mathematical operational semantics and the coalgebraic approach to
weak bisimulation by Brengos. We demonstrate each criterion with various
examples of success and failure and establish a formal connection with the
simply WB cool rule format of Bloom and van Glabbeek. In addition, we show that
the three criteria induce lax models in the sense of Bonchi et al
On the Axiomatisability of Parallel Composition
This paper studies the existence of finite equational axiomatisations of the
interleaving parallel composition operator modulo the behavioural equivalences
in van Glabbeek's linear time-branching time spectrum. In the setting of the
process algebra BCCSP over a finite set of actions, we provide finite,
ground-complete axiomatisations for various simulation and (decorated) trace
semantics. We also show that no congruence over BCCSP that includes
bisimilarity and is included in possible futures equivalence has a finite,
ground-complete axiomatisation; this negative result applies to all the nested
trace and nested simulation semantics