A general conservative extension theorem in process algebras with inequalities

We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc

A Formal Executable Semantics of Verilog

This paper describes a formal executable semantics for the Verilog hardware description language. The goal of our formalization is to provide a concise and mathematically rigorous reference augmenting the prose of the official language standard, and ultimately to aid developers of Verilog-based tools; e.g., simulators, test generators, and verification tools. Our semantics applies equally well to both synthesizeable and behavioral designs and is given in a familiar, operational-style within a logic providing important additional benefits above and beyond static formalization. In particular, it is executable and searchable so that one can ask questions about how a, possibly nondeterministic, Verilog program can legally behave under the formalization. The formalization should not be seen as the final word on Verilog, but rather as a starting point and basis for community discussions on the Verilog semantics.CCF-0916893CNS-0720512CCF-0905584CCF-0448501NNL08AA23Cunpublishedis peer reviewe

Rewriting Logic Semantics of a Plan Execution Language

The Plan Execution Interchange Language (PLEXIL) is a synchronous language developed by NASA to support autonomous spacecraft operations. In this paper, we propose a rewriting logic semantics of PLEXIL in Maude, a high-performance logical engine. The rewriting logic semantics is by itself a formal interpreter of the language and can be used as a semantic benchmark for the implementation of PLEXIL executives. The implementation in Maude has the additional benefit of making available to PLEXIL designers and developers all the formal analysis and verification tools provided by Maude. The formalization of the PLEXIL semantics in rewriting logic poses an interesting challenge due to the synchronous nature of the language and the prioritized rules defining its semantics. To overcome this difficulty, we propose a general procedure for simulating synchronous set relations in rewriting logic that is sound and, for deterministic relations, complete. We also report on two issues at the design level of the original PLEXIL semantics that were identified with the help of the executable specification in Maude

Techniques for Modelling Structured Operational and Denotational Semantics Definitions with Term Rewriting Systems

A fundamental requirement for the application of automatic proof support for program verification is that the semantics of programs be appropriately formalized using the object language underlying the proof tool. This means that the semantics definition must not only be stated as syntactically correct input for the proof tool to be used, but also in such a way that the desired proofs can be performed without too many artificial complications. And it must be clear, of course, that the translation from mathematical metalanguage into the object language is correct. The objective of this work is to present methods for the formalization of structured operational and denotational semantics definitions that meet these requirements. It combines techniques known from implementation of the $\lambda$-calculus with a new way to control term rewriting on object level, thus reaching a conceptually simple representation based on unconditional rewriting. This deduction formalism is available within many of the existent proof tools, and therefore application of the representation methods is not restricted to a particular tool. Correctness of the representations is achieved by proving that the non-trivial formalizations yield results that are equivalent to the meta-level definitions in a strong sense. Since the representation algorithms have been implemented in form of executable programs, there is no need to carry out tedious coding schemes by hand. Semantics definitions can be stated in a format very close to the usual meta language format, and they can be transformed automatically into an object-level representation that is accessible to proof tools. The formalizations of the two semantics definition styles are designed in a consistent way, both making use of the same modelling of the underlying mathematical basis. Therefore, they can be used simultaneously in proofs. This is demonstrated in a larger example, where an operational and a denotational semantics definition for a programming language are proved to be equivalent using the Larch Prover. This proof has been carried out by hand before, and so the characteristics of the automated proof can be made quite clear

Modeling biological systems with delays in Bio-PEPA

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. These semantics of the algebra are given in the Starting-Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. Furthermore we outline how to perform stochastic simulation of Bio-PEPAd systems and how to automatically translate a Bio-PEPAd system into a set of Delay Differential Equations, the deterministic framework for modeling of biological systems with delays. We end the paper with two example models of biological systems with delays to illustrate the approach.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Prototyping Formal System Models with Active Objects

We propose active object languages as a development tool for formal system models of distributed systems. Additionally to a formalization based on a term rewriting system, we use established Software Engineering concepts, including software product lines and object orientation that come with extensive tool support. We illustrate our modeling approach by prototyping a weak memory model. The resulting executable model is modular and has clear interfaces between communicating participants through object-oriented modeling. Relaxations of the basic memory model are expressed as self-contained variants of a software product line. As a modeling language we use the formal active object language ABS which comes with an extensive tool set. This permits rapid formalization of core ideas, early validity checks in terms of formal invariant proofs, and debugging support by executing test runs. Hence, our approach supports the prototyping of formal system models with early feedback.Comment: In Proceedings ICE 2018, arXiv:1810.0205

Thermodynamic graph-rewriting

We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy cost function. The idea is that the generators define the qualitative dynamics, by showing which transformations are possible, while the energy patterns and cost function specify the long-term probability $\pi$ of any reachable graph. Given the generators and energy patterns, we construct a finite set of rules which (i) has the same qualitative transition system as the generators; and (ii) when equipped with suitable rates, defines a continuous-time Markov chain of which $\pi$ is the unique fixed point. The construction relies on the use of site graphs and a technique of `growth policy' for quantitative rule refinement which is of independent interest. This division of labour between the qualitative and long-term quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see the examples in S4 and S5). It also guarantees thermodynamical consistency (AKA detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications

Meta SOS - A Maude Based SOS Meta-Theory Framework

Meta SOS is a software framework designed to integrate the results from the meta-theory of structural operational semantics (SOS). These results include deriving semantic properties of language constructs just by syntactically analyzing their rule-based definition, as well as automatically deriving sound and ground-complete axiomatizations for languages, when considering a notion of behavioural equivalence. This paper describes the Meta SOS framework by blending aspects from the meta-theory of SOS, details on their implementation in Maude, and running examples.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

Specification, simulation, and verification of component connectors in Reo

Coordination and composition of components is an essential concern in component-based software engineering. In this paper, we present an operational semantics for a component composition language called Reo. Reo connectors exogenously compose and coordinate the interactions among individual components, that unawarely comprise a complex system, into a coherent collaboration. The formal semantics we present here paves the way for studying the behavior of component composition mechanisms rigorously. To demonstrate the feasibility of such a rigorous approach, we give a faithful translation of Reo semantics into the Maude term rewriting language. This translation allows us to exploit the rewriting engine and the modelchecking module in the Maude tool-set to symbolically run and model-check the behavior of Reo connectors