Structural Operational Semantics Rules Research Articles

Quantitative extensions of reaction systems based on SOS semantics

Reaction systems (RSs) are a successful natural computing framework inspired by chemical reaction networks. A RS consists of a set of entities and a set of reactions. Entities can enable or inhibit each reaction and are produced by reactions or provided by the environment. In this paper, we define two quantitative variants of RSs: the first one is along the time dimension, to specify delays for making available reactions products and durations to protract their permanency, while the second deals with the possibility to specify different concentration levels of a substance in order to enable or inhibit a reaction. Technically, both extensions are obtained by modifying in a modular way the Structural Operational Semantics (SOS) for RSs that was already defined in the literature. Our approach maintains several advantages of the original semantics definition that were: (1) providing a formal specification of the RS dynamics that enables the reuse of many formal analysis techniques and favours the implementation of tools, and (2) making the RS framework extensible, by adding or changing some of the SOS rules in a compositional way. We provide a prototype logic programming implementation and apply our tool to three different case studies: the tumour growth, the Th cell differentiation in the immune system and neural communication.

A logical and graphical framework for reaction systems

Reaction Systems (RSs) are a successful computational framework inspired by biological systems. A RS pairs a set of entities with a set of reactions over them. Entities can be used to enable or inhibit each reaction, and are produced by reactions. Entities can also be provided by an external context sequence to simulate in silico biological experiments. In this paper we define an extension of RSs considering nondeterministic and recursive context operators, and give an original labelled transition system (LTS) for extended RSs in the structural operational semantics (SOS) style. Thanks to extended contexts, a single LTS can now account for several biological experiments. The rich information recorded in transition labels is useful to guarantee the compositionality of SOS inference rules as well as to define an assertion language to tailor behavioural and logical equivalences on some specific properties or entities. The SOS rules have been also exploited to design a flexible prototype implementation in logic programming that allows to inspect the LTS and to extract useful information when performing experiments on a RS. Our implementation provides a rapid prototyping tool for (extensions of) RSs, with a user friendly online interface to our interpreter. A parser allows to introduce the logical formulas and the contexts using the usual comfortable concrete syntax. The user can visualise and inspect the LTS for a RS and make some analysis of its underlying computation patterns, can check if the main RS satisfies a given property and if it is equivalent to a second adversarial RS. Finally, the SOS approach is suited to drive additional enhancements of RSs.

Implicit Propagation in Structural Operational Semantics

In contrast to a transition system specification in process algebra, a structural operational semantics (SOS) of a programming language usually involves auxiliary entities: stores, environments, etc. When specifying SOS rules, particular auxiliary entities often need to be propagated unchanged between premises and conclusions. The standard technique is to make such propagation explicit, using variables. However, referring to all entities that need to be propagated unchanged in each rule can be tedious, and it hinders direct reuse of rules in different language descriptions. This paper proposes a new interpretation of SOS rules, such that each auxiliary entity is implicitly propagated in all rules in which it is not mentioned. The main benefits include significant notational simplification of SOS rules and much-improved reusability. This new interpretation of SOS rules is based on the same foundations as Modular SOS, but avoids the notational overhead of grouping auxiliary entities together in labels. After motivating and explaining implicit propagation, the paper considers the foundations of SOS and Modular SOS specifications, and defines the meaning of SOS specifications with implicit propagation by translating them to Modular SOS. It then shows how implicit propagation can simplify various rules found in the SOS literature.

A Congruence Rule Format with Universal Quantification

We investigate the addition of universal quantification to the meta-theory of Structural Operational Semantics (SOS). We study the syntax and semantics of SOS rules extended with universal quantification and propose a congruence rule format for strong bisimilarity that supports this new feature.

SOS formats and meta-theory: 20 years after

In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, Aarhus, Denmark, September 1981]. Subsequently, the format of SOS rules became the object of study. Using so-called Transition System Specifications (TSS’s) several authors syntactically restricted the format of rules and showed several useful properties about the semantics induced by any TSS adhering to the format. This has resulted in a line of research proposing several syntactical rule formats and associated meta-theorems. Properties that are guaranteed by such rule formats range from well-definedness of the operational semantics and compositionality of behavioral equivalences to security-, time- and probability-related issues. In this paper, we provide an overview of SOS rule formats and meta-theorems formulated around them.

A Hierarchy of SOS Rule Formats

In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin. A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, Aarhus, Denmark, September 1981. Also published in: Journal of Logic and Algebraic Programming 60–61 (2004) 17–140]. Subsequently, the format of SOS rules became the object of study. Using so-called Transition System Specifications (TSS's) several authors syntactically restricted the format of rules and showed several useful properties about the semantics induced by any TSS adhering to the format. This has resulted in a line of research proposing several syntactical rule formats and associated meta-theorems. Properties that are guaranteed by such rule formats range from well-definedness of the operational semantics and compositionality of behavioral equivalences to security- and probability-related issues. In this paper, we provide an initial hierarchy of SOS rules formats and meta-theorems formulated around them.

Pragmatics of Modular SOS

Modular SOS is a recently-developed variant of Plotkin's Structural Operational Semantics (SOS) framework. It has several pragmatic advantages over the original framework--the most significant being that rules specifying the semantics of individual language constructs can be given <em>definitively</em>, once and for all.<br /> <br />Modular SOS is being used for teaching operational semantics at the undergraduate level. For this purpose, the meta-notation for modular SOS rules has been made more user-friendly, and derivation of computations according to the rules is simulated using Prolog.<br /> <br />After giving an overview of the foundations of Modular SOS, this paper gives some illustrative examples of the use of the framework, and discusses various pragmatic aspects.

Ordered SOS Process Languages for Branching and Eager Bisimulations

We present a general and uniform method for defining structural operational semantics (SOS) of process operators by traditional Plotkin-style transition rules equipped with orderings . This new feature allows one to control the order of application of rules when deriving transitions of process terms. Our method is powerful enough to deal with rules with negative premises and copying. We show that rules with orderings, called ordered SOS rules, have the same expressive power as GSOS rules. We identify several classes of process languages with operators defined by rules with and without orderings in the setting with silent actions and divergence. We prove that branching bisimulation and eager bisimulation relations are preserved by all operators in process languages in the relevant classes.

Ordered SOS Process Languages for Branching and Eager Bisimulations

We present a general and uniform method for defining structural operational semantics (SOS) of process operators by traditional Plotkin-style transition rules equipped with orderings . This new feature allows one to control the order of application of rules when deriving transitions of process terms. Our method is powerful enough to deal with rules with negative premises and copying. We show that rules with orderings, called ordered SOS rules, have the same expressive power as GSOS rules. We identify several classes of process languages with operators defined by rules with and without orderings in the setting with silent actions and divergence. We prove that branching bisimulation and eager bisimulation relations are preserved by all operators in process languages in the relevant classes.

Turning SOS Rules into Equations

Many process algebras are defined by structural operational semantics (SOS). Indeed, most such definitions are nicely structured and fit the GSOS format of Bloom et al. (J. Assoc. Comput. Mach., to appear). We give a procedure for converting any GSOS language definition to a finite complete equational axiom system (possibly with one infinitary induction principle) which precisely characterizes strong bisimulation of processes.