The formal specification of concurrent systems: a small CCS case study

This article describes first steps towards the formal specification and verification of multi-agent systems, through the use of temporal belief logics. The article first describes Concurrent METATEM, a multi-agent programming language, and then develops a logic that may be used to reason about Concurrent METATEM systems. The utility of this logic for specifying and verifying Concurrent METATEM systems is demonstrated through a number of examples. The article concludes with a brief discussion on the wider implications of the work, and in particular on the use of similar logics for reasoning about multi-agent systems in general.

Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature. In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time temporal logics and probabilistic temporal logics. We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.

17 Automata-theoretic techniques for temporal reasoning

Reactive systems are computing systems which are interactive, such as real-time systems, operating systems, concurrent systems and control systems. These are among the most difficult computing systems to program. Temporal logic is a formal tool/language which yields excellent results in specifying reactive systems, and this volume (the first of two), offers an introduction to temporal logic and to the computational model for reactive programs which has been developed by the authors.

Architectures based on Coordinated Atomic action (CA action) concepts have been used to build concurrent fault-tolerant systems. This conceptual model combines concurrent exception handling with action nesting to provide a general mechanism for both enclosing interactions among system components and coordinating forward error recovery measures. This paper proposes an architectural model to guide the formal specification of concurrent fault-tolerant systems. This architecture provides built-in CSP (Communicating Sequential Process) processes and predefined channels to coordinate exception handling of the user-defined components. As a result, a formal and general architecture supporting software fault-tolerance are ready to be used.

We develop a logic-based framework for formal specification and algorithmic verification of homogeneous and dynamic concurrent multi-agent transition systems. Homogeneity means that all agents have the same available actions at any given state and the actions have the same effects regardless of which agents perform them. The state transitions are therefore determined only by the vector of numbers of agents performing each action and are specified symbolically, by means of conditions on these numbers definable in Presburger arithmetic. The agents are divided into controllable (by the system supervisor/controller) and uncontrollable, representing the environment or adversary. Dynamicity means that the numbers of controllable and uncontrollable agents may vary throughout the system evolution, possibly at every transition. As a language for formal specification we use a suitably extended version of Alternating-time Temporal Logic, where one can specify properties of the type “a coalition of (at least) n controllable agents can ensure against (at most) m uncontrollable agents that any possible evolution of the system satisfies a given objective gamma″, where gamma is specified again as a formula of that language and each of n and m is either a fixed number or a variable that can be quantified over. We provide formal semantics to our logic {mathcal {L}}_{textsc {hdmas}} and define normal form of its formulae. We then prove that every formula in {mathcal {L}}_{textsc {hdmas}} is equivalent in the finite to one in a normal form and develop an algorithm for global model checking of formulae in normal form in finite HDMAS models, which invokes model checking truth of Presburger formulae. We establish worst case complexity estimates for the model checking algorithm and illustrate it on a running example.

In an earlier paper by the author, Åqvist (1999), I presented an approach to the logic of historical necessity, or inevitability, in the sense of a “two‐dimensional” combination of tense and modal logic for worlds, or histories, with the same time order, known as T × W logic. Distinctive features of that approach were, apart from its two‐dimensionality, its being based on discrete and finite time, and its use of so‐called systematic frame constants in order to enable us to indicate longitudes (x‐values) and latitudes (y‐values) of any points in the co‐ordinate systems under consideration. This led us to study and axiomatize an infinite hierarchy HTWxy of two‐dimensional modal tense logics with the characteristic operators for historical necessity and possibility added to the original basic vocabulary. The main purpose of the present paper is then twofold: (A) to extend the logics HTWxy to the interesting branch of philosophical logic constituted by deontic logic as combined with tense (or temporal) logic; and (B) to deal with a curious puzzle known as the so‐called epistemic obligation paradox – a well known stumbling‐block in this area of research in philosophical logic. We argue for a solution to both these problems, which appeals to a new infinite hierarchy DHTWxym of extensions of the HTWxy in the sense of logics combining dyadic deontic modalities with temporal ones such as those for historical necessity and other two‐dimensional modalities.

Composition of software artifacts modelled using Colored Petri nets

A good design, development, and maintenance methodology for concurrent systems must be based on a good recognition and/or understanding of the intrinsic characteristics of concurrent systems. Measuring and monitoring the behavior of a complex concurrent system is an indispensable way to achieve the reliability of the system. Based on recognition and/or understanding of the wholeness principle of concurrent systems and the uncertainty principle in measuring and monitoring concurrent systems, the paper proposes a design called the principle, for large-scale, long-lived, and highly reliable concurrent systems. The self-measurement principle requires that a large-scale, long-lived, and highly reliable concurrent system should be constructed by some function components and some (may be only one) permanent self-measurement components that act concurrently with the function components, measure and monitor the system itself according to some requirements, and pass run-time information about the system's behavior to the outside world of the system.

We will begin our study of modal logic with a basic system called K in honor of the famous logician Saul Kripke. K serves as the foundation for a whole family of systems. Each member of the family results from strengthening K in some way. Each of these logics uses its own symbols for the expressions it governs. For example, modal (or alethic) logics use □ for necessity, tense logics use H for what has always been, and deontic logics use O for obligation. The rules of K characterize each of these symbols and many more. Instead of rewriting K rules for each of the distinct symbols of modal logic, it is better to present K using a generic operator. Since modal logics are the oldest and best known of those in the modal family, we will adopt □ for this purpose. So □ need not mean necessarily in what follows. It stands proxy for many different operators, with different meanings. In case the reading does not matter, you may simply call □A ‘box A’.

There are two typical ways to formalize reasoning over time. The first is in a modal logic where time is characterized implicitly through tense operators. The second addresses time explicitly in a first-order theory, where the reasoning is itself essentially first order. In this paper we shall introduce an amalgamated temporal logic which combines the tense operators of the modal approach with the referential aspects of the first-order approach.The modal operators of the new logic, called IQ-C, include the familiar tense operators plus a few new ones; together they allow complex temporal propositions to be represented in a compact form. Unlike standard modal temporal logics, IQ-C contains terms which refer to times; this allows the logic to characterize certain temporal properties and operators which cannot be axiomatized or defined by conventional modal operators. IQ-C is expressively complete over any connected flow of time, and has several other interesting theoretical properties, some of which will be developed in this paper.Most interval logics take one of two approaches to temporal assertions; either they analyze assertions for intervals in terms of assertions at points, or they treat intervals as primitive, allowing assertions for intervals but not at points. IQ-C allows assertions both for intervals and at points, and treats them as independent; this yields a special degree of semantic discrimination and at the same time simplifies the representation of several temporal properties. In this paper we shall outline the IQ-C framework, specifying its special features and defining its semantics. We shall also extend a method of skolemization, which is designed to support a resolution based approach to the proof theory. This will be sketched in some detail, with a view to providing a preliminary account of the basic proof theory. A complete specification of the deductive theory, together with relevant proofs, will be developed elsewhere.KeywordsIntervalsPointsTemporal Representation and ExpressivenessHomogeneitySkolemizationand Modal Theorem Proving

Chapter 4 - Modal Logics and mu-Calculi: An Introduction

The paper presents the LTL preserving stubborn set method for reducing the amount of work needed in the automatic verification of concurrent systems with respect to linear time temporal logic specifications. The method facilitates the generation of reduced state spaces such that the truth values of a collection of linear temporal logic formulas are the same in the ordinary and reduced state spaces. The only restrictions posed by the method are that the collection of formulas must be known before the reduced state space generation is commenced, the use of the temporal operator “next” is prohibited, and the (reduced) state space of the system must be finite. The method cuts down the number of states by utilising the fact that in concurrent systems the nett result of the occurrence of two events is often independent of the order of occurrence.KeywordsLinear Temporal LogicExecution SequenceConcurrent SystemState PredicateLinear Temporal Logic FormulaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We propose a new approach to modelling and reasoning about dynamic networks. Dynamic networks consist of nodes and edges whose operating status may change over time (for example, the edges may be unreliable and operate intermittently). Message-passing in such networks is inherently difficult and reasoning about the behaviour of message-passing algorithms is also difficult. We develop a series of abstract models which allow us to focus on the correctness of routing methods. We model the dynamic network as a ``demonic'' process which runs concurrently with routing updates and message-passing. This allows us to use temporal logic and fairness constraints to reason about dynamic networks. The models are implemented as multi-threaded programs and, to validate them, we use an experimental run-time verification tool called RuleR.

This book is a celebration of Leslie Lamport's work on concurrency, interwoven in four-and-a-half decades of an evolving industry: from the introduction of the first personal computer to an era when parallel and distributed multiprocessors are abundant. His works lay formal foundations for concurrent computations executed by interconnected computers. Some of the algorithms have become standard engineering practice for fault tolerant distributed computing - distributed systems that continue to function correctly despite failures of individual components. He also developed a substantial body of work on the formal specification and verification of concurrent systems, and has contributed to the development of automated tools applying these methods. Part I consists of technical chapters of the book and a biography. The technical chapters of this book present a retrospective on Lamport's original ideas from experts in the field. Through this lens, it portrays their long-lasting impact. The chapters cover timeless notions Lamport introduced: the Bakery algorithm, atomic shared registers and sequential consistency; causality and logical time; Byzantine Agreement; state machine replication and Paxos; temporal logic of actions (TLA). The professional biography tells of Lamport's career, providing the context in which his work arose and broke new grounds, and discusses LaTeX - perhaps Lamport's most influential contribution outside the field of concurrency. This chapter gives a voice to the people behind the achievements, notably Lamport himself, and additionally the colleagues around him, who inspired, collaborated, and helped him drive worldwide impact. Part II consists of a selection of Leslie Lamport's most influential papers. This book touches on a lifetime of contributions by Leslie Lamport to the field of concurrency and on the extensive influence he had on people working in the field. It will be of value to historians of science, and to researchers and students who work in the area of concurrency and who are interested to read about the work of one of the most influential researchers in this field.