Ryszard Janicki

Semantics of inhibitor nets

We discuss an abstract semantics of concurrent systems generalising causal partial orders. The new semantics employs relational structures-called stratified order structures-which comprise causal partial orders and weak causal partial orders. Stratified order structures can be represented by certain equivalence classes of step sequences-comtraces-directly generalising Mazurkiewicz traces. We use Elementary Net Systems with inhibitor arcs as a system model and show that stratified order structures can provide an abstract semantics which is consistent with their operational semantics expressed in terms of step sequences. Two different types of operational rules are considered. We also construct occurrence nets to enable the generation of stratified order structures for a given run of the net.

Structure of concurrency

Abstract Noninterleaving models of concurrency assume that behavioural properties of systems can be adequately modelled in terms of causal partial orders. We claim that the structure of concurrency is richer, with causality being only one of the invariants generated by a set of closely related executions or observations. The model we propose supports three levels of abstraction: the observation level, invariant level and system level; and we will proceed from the bottom (observation) level to the top (system) level. This is in contrast to the way other models for concurrency are introduced, as they essentially support two levels of abstraction, the system level and behavioural level (which includes both observations and invariants), with the direction of development going from the system to behavioural level. In this paper we first discuss the notion of an observation of a concurrent behaviour; in particular, we investigate the role played by interval partial orders. We then introduce a general framework for dealing with invariants generated by sets of closely related observations. This leads to the formulation of the notion of a (concurrent) history whose structural properties are subsequently studied.

On a formal semantics of tabular expressions

Abstract Parnas et al. (Janicki et al., in: Brink, Kahl, Schmidt (Eds.), Relational Methods in Computer Science, Springer, Berlin, 1997; Parnas, Commun. ACM 26 (8) (1983) 572–581; Parnas and Madey, Sci. Comput. Programm. 25 (1) (1995) 41–61; Parnas et al., IEEE Trans. Software Eng. 20 (12) (1994) 948–976) advocate the use of relational model for documenting the intended behaviour of programs. In this method, tabular expressions (or tables) are used to improve readability so that formal documentation can replace conventional documentation. Parnas (CRL Report 260, Telecommunications Research Institute of Ontario (TRIO), Mcmaster University, Hamilton, Ontario, Canada, 1992) describes several classes of tables and provides their formal syntax and semantics. In this paper, an alternative, more general and more homogeneous semantics is proposed. The model covers all known types of tables used in Software Engineering.

Towards a formal semantics of Parnas tables

In Parnas at al. advocate the use of relational model for documenting the intended behaviour of programs. In this method, tabular expressions (or tables) are used to improve readability so that formal documentation can replace conventional documentation. Parnas describes several classes of tables and provides their formal syntax and semantics. In this paper, an alternative, more general and more homogeneous semantics is proposed.

Foundations of the trace assertion method of module interface specification

The trace assertion method is a formal state machine based method for specifying module interfaces. A module interface specification treats the module as a black-box, identifying all the modules access programs (i.e., programs that can be invoked from outside of the module) and describing their externally visible effects. In the method, both the module states and the behaviors observed are fully described by traces built from access program invocations and their visible effects. A formal model for the trace assertion method is proposed. The concept of step-traces is introduced and applied. The stepwise refinement of trace assertion specifications is considered. The role of nondeterminism, normal and exceptional behavior, value functions, and multiobject modules are discussed. The relationship with algebraic specifications is analyzed. A tabular notation for writing trace specifications to ensure readability is adapted.

Invariant Semantics of Nets with Inhibitor Arcs

We here discuss an invariant semantics of concurrent systems which is a generalisation of the causal partial order (CPO) semantics. The new semantics is consistent with the full operational behaviour of inhibitor and priority nets expressed in terms of step sequences. It employs combined partial orders, or composets, where each composet is a relational structure consisting of a causal partial order and a weak causal partial order. In this paper we develop a representation of composets using a novel concept of comtrace, which is certain equivalence class of step sequences. The whole approach resembles to a significant extent the trace semantics introduced by Mazurkiewicz. Composets correspond to posets, comtraces correspond to traces, while step sequences correspond to interleaving sequences. The independency relation is replaced by two new relations. The first is simultaneity which is a symmetric relation comprising pairs of event which may be executed in one step. The other is serialisability which comprises pairs of events (e,f) such that if e and f can be executed in one step then they can also be executed in the order: e followed by f. We show that the comtraces enjoy essentially the same kind of properties as Mazurkiewicz traces, e.g., each comtrace is unambiguously identified by any step sequence which belongs to it. As a system model we consider Elementary Net Systems with Inhibitor Arcs (ENI-systems). We show that the comtrace model provides an invariant semantics for such nets and is in a full agreement with their operational semantics expressed in terms of step sequences. We finally show that the composets represented by comtraces can be generated by generalising the standard construction of a process of a 1-safe Petri net.

Fundamentals of modelling concurrency using discrete relational structures

Abstract.We consider relational structures

Invariants and paradigms of concurrency theory

(X,R_1,R_2)

A formal semantics for concurrent systems with a priority relation

such that

Relational structures model of concurrency

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