Transition System Specifications Research Articles

Lang-n-Send Extended: Sending Regular Expressions to Monitors

In prior work, Cimini has presented Lang-n-Send, a pi-calculus with language definitions. In this paper, we present an extension of this calculus called Lang-n-Send+m. First, we revise Lang-n-Send to work with transition system specifications rather than its language specifications. This revision allows the use of negative premises in deduction rules. Next, we extend Lang-n-Send with monitors and with the ability of sending and receiving regular expressions, which then can be used in the context of larger regular expressions to monitor the execution of programs. We present a reduction semantics for Lang-n-Send+m, and we offer examples that demonstrate the scenarios that our calculus captures.

Synthesising elementary net systems with localities

Elementary net systems with localities (enl-systems) is a class of Petri nets introduced to model globally asynchronous locally synchronous systems (gals), where some of the components can be considered as logically or physically close and acting synchronously, while others can be considered as loosely connected or residing at distant locations and communicating asynchronously with the rest of the system. The specification of the behaviour of a gals system comes very often in the form of a transition system. Automated synthesis based on the regions of transition systems is an approach that allows to construct Petri net models from their transition system specifications. In this paper we focus on developing algorithms and tool support for the synthesis of the enl-systems from transition systems, where transitions are labelled by steps (sets) of executed actions. We pay special attention to the subclass of enl-systems with localised conflicts where there is no conflict between events belonging to different localities. The algorithms are implemented within the workcraft framework.

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 $\alpha$-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.

Divide and congruence III: From decomposition of modal formulas to preservation of stability and divergence

In two earlier papers we derived congruence formats with regard to transition system specifications for weak semantics on the basis of a decomposition method for modal formulas. The idea is that a congruence format for a semantics must ensure that the formulas in the modal characterisation of this semantics are always decomposed into formulas that are again in this modal characterisation. The stability and divergence requirements that are imposed on many of the known weak semantics have so far been outside the realm of this method. Stability refers to the absence of a τ-transition. We show, using the decomposition method, how congruence formats can be relaxed for weak semantics that are stability-respecting. This relaxation for instance brings the priority operator within the range of the stability-respecting branching bisimulation format. Divergence, which refers to the presence of an infinite sequence of τ-transitions, escapes the inductive decomposition method. We circumvent this problem by proving that a congruence format for a stability-respecting weak semantics is also a congruence format for its divergence-preserving counterpart.

Refining autonomous agents with declarative beliefs and desires

Abstract An autonomous agent is one that is not only directed by its environment, but is also driven by internal motivation to achieve certain goals based on beliefs about the environmental behaviour. Design paradigms for autonomous agents such as belief-desire-intention take into account the agent’s “mental” features when presenting its patterns of behaviour. In this paper we present an approach to modelling autonomous agents by introducing mental features to conventional transition system specifications. Mental features such as belief and desire are represented by declarative linear temporal logic formulas. Refinement is then proposed to define the correctness of the agent design and development. It turns out, however, that the introduction of these mental features is not monotonic with respect to refinement. We therefore introduce additional refinement proof obligations to enable the use of simulation rules when checking refinement.

Rooted branching bisimulation as a congruence for probabilistic transition systems

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.

SOS rule formats for convex and abstract probabilistic bisimulations

Probabilistic transition system specifications (PTSSs) in the $nt \mu f\theta / nt\mu x\theta$ format provide structural operational semantics for Segala-type systems that exhibit both probabilistic and nondeterministic behavior and guarantee that bisimilarity is a congruence for all operator defined in such format. Starting from the $nt \mu f\theta / nt\mu x\theta$ format, we obtain restricted formats that guarantee that three coarser bisimulation equivalences are congruences. We focus on (i) Segala's variant of bisimulation that considers combined transitions, which we call here "convex bisimulation"; (ii) the bisimulation equivalence resulting from considering Park & Milner's bisimulation on the usual stripped probabilistic transition system (translated into a labelled transition system), which we call here "probability obliterated bisimulation"; and (iii) a "probability abstracted bisimulation", which, like bisimulation, preserves the structure of the distributions but instead, it ignores the probability values. In addition, we compare these bisimulation equivalences and provide a logic characterization for each of them.

Bisimulation proof methods in a path-based specification language for polynomial coalgebras

What reasoning rules can be used for the deduction of bisimulation formulas in coalgebraic specifications is problematic because those rules used in algebraic specifications possibly cannot be applied to bisimulation formulas. Although some categorical bisimulation proof methods for coalgebras have been proposed, they are not based on specification languages of coalgebras so that they cannot be used as reasoning rules. In this paper, a specification language based on paths of polynomial functors is proposed to specify polynomial coalgebras. Paths of polynomial functors give detailed observations and transitions on the state space of coalgebras so that the techniques used in transition system specifications can be applied to such a path-based language. In particular, because bisimulations can be characterized by paths, the notions of progressions, respectful functions and faithful contexts can be defined based on paths, and then bisimulation up-to proof techniques, including bisimulation up-to bisimilarities and up-to contexts for transition systems can be transformed into reasoning rules in the language. Several examples illustrate how to reason syntactically about bisimulations in the language by using the rules induced by the bisimulation proof techniques.

Compositionality of Approximate Bisimulation for Probabilistic Systems

Probabilistic transition system specifications using the rule format ntmuft-ntmuxt provide structural operational semantics for Segala-type systems and guarantee that probabilistic bisimilarity is a congruence. Probabilistic bisimilarity is for many applications too sensitive to the exact probabilities of transitions. Approximate bisimulation provides a robust semantics that is stable with respect to implementation and measurement errors of probabilistic behavior. We provide a general method to quantify how much a process combinator expands the approximate bisimulation distance. As a direct application we derive an appropriate rule format that guarantees compositionality with respect to approximate bisimilarity. Moreover, we describe how specification formats for non-standard compositionality requirements may be derived.

Tree rules in probabilistic transition system specifications with negative and quantitative premises

Probabilistic transition system specifications (PTSSs) in the ntmufnu/ntmuxnu format provide structural operational semantics for Segala-type systems that exhibit both probabilistic and nondeterministic behavior and guarantee that isimilarity is a congruence.Similar to the nondeterministic case of rule format tyft/tyxt, we show that the well-foundedness requirement is unnecessary in the probabilistic setting. To achieve this, we first define an extended version of the ntmufnu/ntmuxnu format in which quantitative premises and conclusions include nested convex combinations of distributions. This format also guarantees that bisimilarity is a congruence. Then, for a given (possibly non-well-founded) PTSS in the new format, we construct an equivalent well-founded transition system consisting of only rules of the simpler (well-founded) probabilistic ntree format. Furthermore, we develop a proof-theoretic notion for these PTSSs that coincides with the existing stratification-based meaning in case the PTSS is stratifiable. This continues the line of research lifting structural operational semantic results from the nondeterministic setting to systems with both probabilistic and nondeterministic behavior.

Congruence from the Operator's Point of View: Compositionality Requirements on Process Semantics

One of the basic sanity properties of a behavioural semantics is that it constitutes a congruence with respect to standard process operators. This issue has been traditionally addressed by the development of rule formats for transition system specifications that define process algebras. In this paper we suggest a novel, orthogonal approach. Namely, we focus on a number of process operators, and for each of them attempt to find the widest possible class of congruences. To this end, we impose restrictions on sublanguages of Hennessy-Milner logic, so that a semantics whose modal characterization satisfies a given criterion is guaranteed to be a congruence with respect to the operator in question. We investigate action prefix, alternative composition, two restriction operators, and parallel composition.

Contracts for modular discrete controller synthesis

We describe the extension of a reactive programming language with a behavioral contract construct. It is dedicated to the programming of reactive control of applications in embedded systems, and involves principles of the supervisory control of discrete event systems. Our contribution is in a language approach where modular discrete controller synthesis (DCS) is integrated, and it is concretized in the encapsulation of DCS into a compilation process. From transition system specifications of possible behaviors, DCS automatically produces controllers that make the controlled system satisfy the property given as objective. Our language features and compiling technique provide correctness-by-construction in that sense, and enhance reliability and verifiability. Our application domain is adaptive and reconfigurable systems: closed-loop adaptation mechanisms enable flexible execution of functionalities w.r.t. changing resource and environment conditions. Our language can serve programming such adaption controllers. This paper particularly describes the compilation of the language. We present a method for the modular application of discrete controller synthesis on synchronous programs, and its integration in the BZR language. We consider structured programs, as a composition of nodes, and first apply DCS on particular nodes of the program, in order to reduce the complexity of the controller computation; then, we allow the abstraction of parts of the program for this computation; and finally, we show how to recompose the different controllers computed from different abstractions for their correct co-execution with the initial program. Our work is illustrated with examples, and we present quantitative results about its implementation.

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.

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.

Prototyping SOS Meta-theory in Maude

We present a prototype implementation of SOS meta-theory in the Maude term rewriting language. The prototype defines the basic concepts of SOS meta-theory (e.g., transition formulae, deduction rules and transition system specifications) in Maude. Besides the basic definitions, we implement methods for checking the premises of some SOS meta-theorems (e.g., GSOS congruence meta-theorem) in this framework. Furthermore, we define a generic strategy for animating programs and models for semantic specifications in our meta-language. The general goal of this line of research is to develop a general-purpose tool that assists language designers by checking useful properties about the language under definition and by providing a rapid prototyping environment for scrutinizing the actual behavior of programs according to the defined semantics.

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.

The meaning of negative premises in transition system specifications II

This paper reviews several methods to associate transition relations to transition system specifications with negative premises in Plotkin's structural operational style. Besides a formal comparison on generality and relative consistency, the methods are also evaluated on their taste in determining which specifications are meaningful and which are not. Additionally, this paper contributes a proof theoretic characterisation of the well-founded semantics for logic programs.

Precongruence formats for decorated trace semantics

This paper explores the connection between semantic equivalences and preorders for concrete sequential processes, represented by means of labeled transition systems, and formats of transition system specifications using Plotkin's structural approach. For several preorders in the linear time---branching time spectrum a format is given, as general as possible, such that this preorder is a precongruence for all operators specifiable in that format. The formats are derived using the modal characterizations of the corresponding preorders.

Syntactic Formats for Free: An Abstract Approach to Process Equivalence

A framework of Plotkin and Turis, 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 deriving syntactic formats for transition system specifications, which guarantee operational preorders to be precongruences. The technique is applied to the trace prorder, the completed trace preorder and the failures preorder. In the latter two cases, new syntactic formats guaranteeing precongruence properties are introduced.

A format for semantic equivalence comparison

This paper presents a new format for process algebras, the extended tyft/tyxt format which generalises the tyft/tyxt format of Groote and Vaandrager. The format differs from most previous formats in that the labels on transitions are treated as many-sorted terms. Bisimulation is a congruence for all operators defined by extended transition system specifications in this format. When one extended transition system specification is summed with another, the resulting bisimulation can either identify more terms (an abstracting extension up to bisimulation) or fewer terms (a refining extension up to bisimulation) than the original bisimulation on the individual system. The notions of abstracting extension and refining extension are defined, and two theorems are presented giving conditions required for achieving each type of extension. These results provide a way to compare different semantic equivalences defined for different process algebras. Finally, an application of this theory to semantic equivalence comparison is given for a new result relating Castellani's pomset equivalence and Krishnan's multiprocessor equivalence.