34 research outputs found
A general account of coinduction up-to
Bisimulation up-to enhances the coinductive proof method for bisimilarity, providing efficient proof techniques for checking properties of different kinds of systems. We prove the soundness of such techniques in a fibrational setting, building on the seminal work of Hermida and Jacobs. This allows us to systematically obtain up-to techniques not only for bisimilarity but for a large class of coinductive predicates modeled as coalgebras. The fact that bisimulations up to context can be safely used in any language specified by GSOS rules can also be seen as an instance of our framework, using the well-known observation by Turi and Plotkin that such languages form bialgebras. In the second part of the paper, we provide a new categorical treatment of weak bisimilarity on labeled transition systems and we prove the soundness of up-to context for weak bisimulations of systems specified by cool rule formats, as defined by Bloom to ensure congruence of weak bisimilarity. The weak transition systems obtained from such cool rules give rise to lax bialgebras, rather than to bialgebras. Hence, to reach our goal, we extend the categorical framework developed in the first part to an ordered setting
Up-to Techniques for Branching Bisimilarity
Ever since the introduction of behavioral equivalences on processes one has
been searching for efficient proof techniques that accompany those
equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by
an arsenal of up-to techniques: enhancements of their proof methods. For
branching bisimilarity, these results have not been established yet. We show
that a powerful proof technique is sound for branching bisimilarity by
combining the three techniques of up to union, up to expansion and up to
context for Bloom's BB cool format. We then make an initial proposal for
casting the correctness proof of the up to context technique in an abstract
coalgebraic setting, covering branching but also {\eta}, delay and weak
bisimilarity
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
Axiomatizing Prefix Iteration with Silent Steps
Prefix iteration is a variation on the original binary version of the Kleene star operation P*Q, obtained by restricting the first argument to be an atomic action. The interaction of prefix iteration with silent steps is studied in the setting of Milner's basic CCS. Complete equational axiomatizations are given for four notions of behavioural congruence over basic CCS with prefix iteration, viz. branching congruence, eta-congruence, delay congruence and weak congruence. The completeness proofs for eta-, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence. It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature. The preliminaries and the completeness proofs focus on open terms, i.e. terms that may contain process variables. As a by-product, the omega-completeness of the axiomatizations is obtained as well as their completeness for closed terms. AMS Subject Classification (1991): 68Q10, 68Q40, 68Q55.CR Subject Classification (1991): D.3.1, F.1.2, F.3.2.Keywords and Phrases: Concurrency, process algebra, basic CCS, prefix iteration, branching bisimulation, eta-bisimulation, delay bisimulation, weak bisimulation, equational logic, complete axiomatizations
Lean and Full Congruence Formats for Recursion
In this paper I distinguish two (pre)congruence requirements for semantic
equivalences and preorders on processes given as closed terms in a system
description language with a recursion construct. A lean congruence preserves
equivalence when replacing closed subexpressions of a process by equivalent
alternatives. A full congruence moreover allows replacement within a recursive
specification of subexpressions that may contain recursion variables bound
outside of these subexpressions.
I establish that bisimilarity is a lean (pre)congruence for recursion for all
languages with a structural operational semantics in the ntyft/ntyxt format.
Additionally, it is a full congruence for the tyft/tyxt format.Comment: To appear in: Proc. LICS'17, Reykjavik, Iceland, IEE
Rooted branching bisimulation as a congruence for probabilistic transition systems
Ponencia presentada en el 13 International Workshop on Quantitative Aspects of Programming Languages and Systems. London, United Kingdom, April 11-12, 2015.We propose a probabilistic transition system specification format, referred to as probabilistic RBB safe, for which rooted branching bisimulation is a congruence. The congruence theorem is based on the approach of Fokkink for the qualitative case. For this to work, the theory of transition system specifications in the setting of labeled transition systems needs to be extended to deal with probability distributions, both syntactically and semantically. We provide a scheduler-free characterization of probabilistic branching bisimulation as adapted from work of Andova et al. for the alternating model. Counter examples are given to justify the various conditions required by the format.Fil: Lee, Matías David. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: De Vink, Erik P. Eindhoven University of Technology; The Netherlands.Fil: De Vink, Erik P. Centrum Wiskunde & Informatica; The Netherlands.Ciencias de la Computació
A Declarative Validator for GSOS Languages
Rule formats can quickly establish meta-theoretic properties of process
algebras. It is then desirable to identify domain-specific languages (DSLs)
that can easily express rule formats. In prior work, we have developed
Lang-n-Change, a DSL that includes convenient features for browsing language
definitions and retrieving information from them. In this paper, we use
Lang-n-Change to write a validator for the GSOS rule format, and we augment
Lang-n-Change with suitable macros on our way to do so. Our GSOS validator is
concise, and amounts to a few lines of code. We have used it to validate
several concurrency operators as adhering to the GSOS format. Moreover, our
code expresses the restrictions of the format declaratively.Comment: In Proceedings PLACES 2023, arXiv:2304.0543
The Way We Were: Structural Operational Semantics Research in Perspective
This position paper on the (meta-)theory of Structural Operational Semantic
(SOS) is motivated by the following two questions: (1) Is the (meta-)theory of
SOS dying out as a research field? (2) If so, is it possible to rejuvenate this
field with a redefined purpose?
In this article, we will consider possible answers to those questions by
first analysing the history of the EXPRESS/SOS workshops and the data
concerning the authors and the presentations featured in the editions of those
workshops as well as their subject matters.
The results of our quantitative and qualitative analyses all indicate a
diminishing interest in the theory of SOS as a field of research. Even though
`all good things must come to an end', we strive to finish this position paper
on an upbeat note by addressing our second motivating question with some
optimism. To this end, we use our personal reflections and an analysis of
recent trends in two of the flagship conferences in the field of Programming
Languages (namely POPL and PDLI) to draw some conclusions on possible future
directions that may rejuvenate research on the (meta-)theory of SOS. We hope
that our musings will entice members of the research community to breathe new
life into a field of research that has been kind to three of the authors of
this article.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.0578