Sigurd Meldal

Algebraic approaches to nondeterminism—an overview

Mathematics never saw much of a reason to deal with something called nondeterminism. It works with values, functions, sets, and relations. In computing science, however, nondeterminism has been an issue from the very beginning, if only in the form of nondeterministic Turing machines or nondeterministic finite state machines. Early references to nondeterminism in computer science go back to the 1960s [Floyd 1967; McCarthy 1963]. A great variety of theories and formalisms dealing with it have been developed during the last two decades. There are the denotational models based on power domains, the predicate transformers for the choice construct, and modifications of the l-calculus [de Liguoro and Piperno 1992; Astesiano and Costa 1979; Hennessy 1980]. Nondeterminism arises in a natural way when discussing concurrency, and models of concurrency typically also model nondeterminism. There are numerous variants of process languages and algebra, event structures, state transition systems [Manna and Pnueli 1992; Lehmann and Shelah 1983], and Petri nets [Petri 1977; Reisig 1985]. In terms of modeling, nondeterminism may be considered a purely operational notion. However, one of the main reasons for considering nondeterminism in computer science is the need for abstraction, allowing one to disregard irrelevant aspects of actual computations. Typically, we prefer to work with models that do not include all the details of the physical environment of computations such as timing, temperature, representation on hardware, and the like. Since we do not want to model all these complex dependencies, we may instead represent them by nondeterministic choices. The nondeterminism of concurrent systems usually arises as an ab-

An extension of standard ML modules with subtyping and inheritance

We describe a general module language integrating abstract data types, specifications and object-oriented concepts. The framework is based on the Standard ML module system, with three main extensions: subtyping, a form of object derived from ML structures, and inherit ante primitives. The language aims at supporting a range of programming styles, including mixtures of object-oriented programming and programs built around specified algebraic or higher-order abstract data types. We separate specification from implementation, and provide independent inheritance mechanisms for each. In order to support binary operations on objects within this framework, we introduce “internal interfaces” which govern the way that function components of one structure may access components of another. The language design has been tested by writing a number of program examples; an implementation is under development in the context of a larger project.

Exploiting locality in maintaining potential causality

In distributed systems it is often important to be able to determine the temporal relationships between events generated by different processes. An algorithm to determiue such relationships is presented in [3] and [5]. This algorithm has many favorable attributes such as it allows for any kind of interprocess communication, and it requires no extra synchronization messages, additional communication links or cent ral t imestamping authority. The algorithm, however, requires O(n) space for each process (where n is the number of processes). i.e., it requires an overall space of 0(n2 ). This can be a large overhead especially when there are a very large number of processes. By cutting down on this generality, we can significantly decrease the amount of space required to determine temporal relationships. In this paper, we show how one may reduce the space requirements by assuming that the communication links between processes is static and known ahead oj time; and also that one is interested only in determining the temporal ordering between messages arriving at the same process. We argue that these assumptions are reasonable to make for a large class of problems.

A complete calculus for the multialgebraic and functional semantics of nondeterminism

The current algebraic models for nondeterminism focus on the notion of possibility rather than necessity and consequently equate (nondeterministic) terms that one would intuitively not consider equal. Furthermore, existing models for nondeterminism depart radically from the standard models for (equational) specifications of deterministic operators. One would prefer that a specification language for nondeterministic operators be based on an extension of the standard model concepts, preferably in such a way that the reasoning system for (possibly nondeterministic) operators becomes the standard equational one whenever restricted to the deterministic operators—the objective should be to minimize the departure from the standard frameworks. In this article we define a specification language for nondeterministic operators and multialgebraic semantics. The first complete reasoning system for such specifications is introduced. We also define a transformation of specifications of nondeterministic operators into derived specifications of deterministic ones, obtaining a “computational” semantics of nondeterministic specification by adopting the standard semantics of the derived specification as the semantics of the original one. This semantics turns out to be a refinement of multialgebra semantics. The calculus is shown to be sound and complete also with respect to the new semantics.

Multialgebras, Power Algebras and Complete Calculi of Identities and Inclusions

After motivating the introduction of nondeterministic operators into algebraic specifications, a language L with two primitive predicates, identity and inclusion, for specifying nondeterministic operations is introduced. It is given a multialgebraic semantics which captures the singular (call-time-choice) strategy of passing nondeterministic parameters. A calculus NEQ, with restricted substitutivity rules, is introduced. NEQ is sound and complete wrt. the multialgebraic semantics.

Measuring Component-Based Systems Using a Systematic Approach and Environment

SOA applications are developed to implement service-oriented workflows with service specifications. Most SOA applications are made of service-oriented components, which are built using standard specifications and interaction protocols. How to validate system performance and measure the non-function requirements and behaviors in a component-based SOA application becomes a challenge for engineer. This paper focuses on the measurement of the component-based SOA systems in terms of service-oriented process speed, system reliability, throughput, and availability. The paper proposes a systematic solution to support the system level measurement for component-based SOA software, which extends our previous component level performance measurement. The paper presents a systematic solution using an event-based functional transition model as a performance evaluation model, and its evaluation metrics, such as system processing time, throughput, availability and reliability. It reports the basic functions and design of this solution, also presents a case study and application results

An axiomatic semantics for nested concurrency

We give transformation rules for the concurrent parts of Hoares language CSP, transforming concurrent CSP programs into nondeterministic, sequential programs.On the basis of these transformations we define an axiomatic semantics for CSP with nested concurrency.This axiomatic system includes a rule for binary, associative process composition, enabling modular verification dealing with parts of concurrent systems as well as full programs.The proof system is fully abstract, in the sense that the internal structure of processes is irrelevant in the specification inasmuch it is not externally observable.An outline of a verification of a recursive, concurrent sorter is given as an example.

Partial correctness of exits from concurrent structures

A rudimentary exit-mechanism from the parallel command of the language fragment CSP is introduced. A method for embedding invariants in a standard partial correctness system with pre-and postconditions is presented. Proof rules for exits from concurrent systems are introduced, and a simple data flow system is verified.

Singular and Plural Nondeterministic Parameters

The article defines algebraic semantics of singular (call-time-choice) and plural (run-time-choice) nondeterministic parameter passing and presents a specification language in which operations with both kinds of parameters can be defined simultaneously. Sound and complete calculi for both semantics are introduced. We study the relations between the two semantics and point out that axioms for operations with plural arguments may be considered as axiom schemata for operations with singular arguments.

Generated Models and the omega-Rule: The Nondeterministic Case

A language for specifying nondeterministic operations which generalizes the equational specification language is introduced. Then, various notions of generated multimodels are discussed and sufficient conditions for the existence of quasi-initial semantics of nondeterministic specifications are given. Two calculi are introduced: NEQ and NIP. The former is sound and complete with respect to the class of all multimodels. The latter is an extension of the former with the ω-rule. It is sound and complete with respect to one of the classes of the generated multimodels. The calculi reduce to the respective deterministic calculi whenever the specification involves only deterministic operations.