Bartek Klin

Structural operational semantics for stochastic process calculi

A syntactic framework called SGSOS, for defining well-behaved Markovian stochastic transition systems, is introduced by analogy to the GSOS congruence format for nondeterministic processes. Stochastic bisimilarity is guaranteed a congruence for systems defined by SGSOS rules. Associativity of parallel composition in stochastic process algebras is also studied within the framework.

Coalgebraic Modal Logic Beyond Sets

Polyadic coalgebraic modal logic is studied in the setting of locally presentable categories. It is shown that under certain assumptions, accessible functors admit expressive logics for their coalgebras. Examples include typical functors used to describe systems with name binding, interpreted in nominal sets.

Semantics of Architectural Specifications in CASL

We present a semantics for architectural specifications in CASL, including an extended static analysis compatible with model-theoretic requirements. The main obstacle here is the lack of amalgamation for CASL models. To circumvent this problem, we extend the CASL logic by introducing enriched signatures, where subsort embeddings form a category rather than just a preorder. The extended model functor has amalgamation, which makes it possible to express the amalgamability conditions in the semantic rules in static terms. Using these concepts, we develop the semantics at various levels in an institution-independent fashion.

Checking Amalgamability Conditions for C ASL Architectural Specifications

CASL, a specification formalism developed recently by the CoFI group, offers architectural specifications as a way to describe how simpler modules can be used to construct more complex ones. The semantics for Casl architectural specifications formulates static amalgamation conditions as a prerequisite for such constructions to be well-formed. These are non-trivial in the presence of subsorts due to the failure of the amalgamation property for the Casl institution. We show that indeed the static amalgamation conditions for Casl are undecidable in general. However, we identify a number of practically relevant special cases where the problem becomes decidable and analyze its complexity there. In cases where the result turns out to be PSPACE-hard, we discuss further restrictions under which polynomial algorithms become available. All this underlies the static analysis as implemented in the Casl tool set.

From Bialgebraic Semantics to Congruence Formats

A general and abstract framework to defining congruence formats for various process equivalences is presented. The framework extends bialgebraic techniques of Turi and Plotkin with an abstract coalgebraic approach to process equivalence, based on a notion of test suite. The resulting technique is illustrated on the example of completed trace equivalence. Rather than providing formal proofs, the paper is guiding the reader through the process of deriving a congruence format in the test suite approach.

Bialgebraic Methods in Structural Operational Semantics

Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about well-behaved structural operational specifications. An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this talk, the current state of the art in the area of bialgebraic semantics is presented, and its prospects for the future are sketched. In particular, a combination of basic bialgebraic techniques with a categorical approach to modal logic is described, as an abstract approach to proving compositionality by decomposing modal logics over structural operational specifications.

Amalgamation in the semantics of CASL

We present a semantics for architectural specifications in the Common Algebraic Specification Language (CASL), including an extended static analysis compatible with model-theoretic requirements. The main obstacle here is the lack of amalgamation for CASL models. To circumvent this problem, we extend the CASL logic by introducing enriched signatures, where subsort embeddings form a category rather than just a preorder. The extended model functor satisfies the amalgamation property as well as its converse, which makes it possible to express the amalgamability conditions in the semantic rules in static terms. Using these concepts, we develop the semantics at various levels in an institution-independent fashion. Moreover, amalgamation for enriched CASL means that a variety of results for institutions with amalgamation, such as computation of normal forms and theorem proving for structured specifications, can now be used for CASL.

Bialgebraic Operational Semantics and Modal Logic

A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by structural operational semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived from the corresponding sets for its subprocesses, then the logical equivalence is a congruence. Striving for generality, SOS rules are modeled categorically as bialgebraic distributive laws for some notions of process syntax and behaviour, and modal logics are modeled via coalgebraic polyadic modal logic. Compositionality is proved by providing a suitable notion of behaviour for the logic together with a dual distributive law, reflecting the one modeling the SOS specification. Concretely, the dual laws may appear as SOS-like rules where logical formulas play the role of processes, and their behaviour models logical decomposition over process syntax. The approach can be used either to proving compositionality for specific languages or for defining SOS congruence formats.

Syntactic Formats for Free

A framework of Plotkin and Turi’s, originally aimed at providing an abstract notion of bisimulation, is modified to cover other operational equivalences and preorders. Combined with bialgebraic methods, it yields a technique for the derivation of syntactic formats for transition system specifications which guarantee operational preorders to be precongruences. The technique is applied to the trace preorder, the completed trace preorder and the failures preorder. In the latter two cases, new syntactic formats ensuring precongruence properties are introduced.

Expressiveness of Probabilistic Modal Logics, Revisited

Labelled Markov processes are probabilistic versions of labelled transition systems. In general, the state space of a labelled Markov process may be a continuum. Logical characterizations of probabilistic bisimulation and simulation were given by Desharnais et al. These results hold for systems defined on analytic state spaces and assume that there are countably many labels in the case of bisimulation and finitely many labels in the case of simulation. In this paper, we first revisit these results by giving simpler and more streamlined proofs. In particular, our proof for simulation has the same structure as the one for bisimulation, relying on a new result of a topological nature. This departs from the known proof for this result, which uses domain theory techniques and falls out of a theory of approximation of Labelled Markov processes. Both our proofs assume the presence of countably many labels. We investigate the necessity of this assumption, and show that the logical characterization of bisimulation may fail when there are uncountably many labels. However, with a stronger assumption on the transition functions (continuity instead of just measurability), we can regain the logical characterization result, for arbitrarily many labels. These new results arose from a new game-theoretic way of understanding probabilistic simulation and bisimulation.