Algebraic Specification Research Articles

AUTOMATIC INITIAL SEGMENTATION OF SPEECH SIGNAL BASED ON SYMMETRIC MATRIX OF DISTANCES

The most common issue of a speech signals analisys and artificial intelligence systems development is determining of temporal and frequency charactristics. That’s because any undetermined signal is defined as a nonlinear object. But it is always possible to select time interval from the signals with a given discretization period. Such an interval is called quasistationary interval.The quasistationary interval in combination with the speech signal quality characteristics can be used to build a parametric model of the speech signal. As a result, such a model will be very helpful for solving different issues of artificial intelligence development processes.In this paper the method of an initial segmentation of the speech signal via quasistationary intervals by threshold deviation of algebraic specifications of elementary areas is presented. The latter method of automatic initial segmentation is based on pseudorotation of symmetric matrix of distances and evaluation criteria. The problem and process of selection the quasistationary intervals are described in the section 1.

Order-sorted equality enrichments modulo axioms

Built-in equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications with initial algebra semantics beyond the pale of theorem proving tools based, for example, on explicit or inductionless induction techniques, and of other formal tools for checking key properties such as confluence, termination, and sufficient completeness. Such specifications would instead be amenable to formal analysis if an equationally-defined equality predicate enriching the algebraic data types were to be added to them. Furthermore, having an equationally-defined equality predicate is very useful in its own right, particularly in inductive theorem proving. Is it possible to effectively define a theory transformation E↦E∼ that extends an algebraic specification E to a specification E∼ having an equationally-defined equality predicate? This paper answers this question in the affirmative for a broad class of order-sorted conditional specifications E that are sort-decreasing, ground confluent, and operationally terminating modulo axioms B and have a subsignature of constructors. The axioms B can consist of associativity, or commutativity, or associativity–commutativity axioms, so that the constructors are free modulo B. We prove that the transformation E↦E∼ preserves all the just-mentioned properties of E. The transformation has been automated in Maude using reflection and is used as a component in many Maude formal tools.

The role of logical interpretations in program development

Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant transformations in the context of software design, reuse, and adaptation. This paper proposes a new approach to refinement in which signature morphisms are replaced by logical interpretations as a means to witness refinements. The approach is first presented in the context of equational logic, and later generalised to deductive systems of arbitrary dimension. This allows, for example, refining sentential into equational specifications and the latter into modal ones.

Investigation of Formal Methods Based on Algebraic Specifications for Sensor Systems

Investigation of Formal Methods Based on Algebraic Specifications for Sensor Systems

Categorical Semantics of Reference Data Type

Reference types are very useful structures enabling handling with dynamic memory. In this paper we extend categorical model of type system with reference data type. We illustrate our approach on simple functional programming language T-NBL extended with reference type. After constructing parametric algebraic specification we construct categorical model of reference type and we show how our results can be implemented in functional programming language Ocaml.

Equality to Equals and Unequals: A Revisit of the Equivalence and Nonequivalence Criteria in Class-Level Testing of Object-Oriented Software

Algebraic specifications have been used in the testing of object-oriented programs and received much attention since the 1990s. It is generally believed that class-level testing based on algebraic specifications involves two independent aspects: the testing of equivalent and nonequivalent ground terms. Researchers have cited intuitive examples to illustrate the philosophy that even if an implementation satisfies all the requirements specified by the equivalence of ground terms, it may still fail to satisfy some of the requirements specified by the nonequivalence of ground terms. Thus, both the testing of equivalent ground terms and the testing of nonequivalent ground terms have been considered as significant and cannot replace each other. In this paper, we present an innovative finding that, given any canonical specification of a class with proper imports, a complete implementation satisfies all the observationally equivalent ground terms if and only if it satisfies all the observationally nonequivalent ground terms. As a result, these two aspects of software testing cover each other and can therefore replace each other. These findings provide a deeper understanding of software testing based on algebraic specifications, rendering the theory more elegant and complete. We also highlight a couple of important practical implications of our theoretical results.

Yield grammar analysis and product optimization in a domain-specific language for dynamic programming

Dynamic programming algorithms are traditionally expressed by a set of matrix recurrences—a low level of abstraction, which renders the design of novel dynamic programming algorithms difficult and makes debugging cumbersome.Bellman's GAP is a declarative, domain-specific language, which supports dynamic programming over sequence data. It implements the algebraic style of dynamic programming and allows one to specify algorithms by combining so-called yield grammars with evaluation algebras. Products on algebras allow to create novel types of analyses from already given ones, without modifying tested components. Bellman's GAP extends the previous concepts of algebraic dynamic programming in several respects, such as an “interleaved” product operation and the analysis of multi-track input.Extensive analysis of the yield grammar and the evaluation algebras is required for generating efficient imperative code from the algebraic specification. This article gives an overview of the analyses required and presents several of them in detail. Measurements with “real-world” applications demonstrate the quality of the code produced.

On the whereabouts of CSP-CASL – A survey

C SP -C ASL is but one of the many languages for which Bernd Krieg-Brueckner (BKB) had a great deal of influence throughout its development process: from the initial idea of working towards an integration of the process algebra C SP with the algebraic specification language C ASL , to the design of the concrete syntax, and also to tool support for C SP -C ASL , where the theorem prover Isabelle should provide the common platform. In all this, BKB provided inspiration and guidance, funding, and also a helping hand when needed. This paper provides a survey on the technology developed so far for C SP -C ASL , covering results of a theoretical nature, an industrial case study, theorem proving support as well as a testing approach. In honour of BKB’s 60th birthday, this survey documents what has become out of one of BKB’s visions.

A Coalgebraic Perspective on Logical Interpretations

In Computer Science stepwise refinement of algebraic specifications is a well-known formal methodology for rigorous program development. This paper illustrates how techniques from Algebraic Logic, in particular that of interpretation, understood as a multifunction that preserves and reflects logical consequence, capture a number of relevant transformations in the context of software design, reuse, and adaptation, difficult to deal with in classical approaches. Examples include data encapsulation and the decomposition of operations into atomic transactions. But if interpretations open such a new research avenue in program refinement, (conceptual) tools are needed to reason about them. In this line, the paper's main contribution is a study of the correspondence between logical interpretations and morphisms of a particular kind of coalgebras. This opens way to the use of coalgebraic constructions, such as simulation and bisimulation, in the study of interpretations between (abstract) logics.

Compositionally Writing Proof Scores of Invariants in the OTS/CafeOBJ Method

Observational transition systems (OTSs) are state machines that can be described as behavioral specifications in CafeOBJ, an algebraic specification language and processor. The OTS/CafeOBJ method uses OTSs and CafeOBJ for systems spec- ification and verification. Simultaneous induction is intensively used to prove that an OTS enjoys invariants in the method. To prove that two state predicates p and q are invariants with respect to an OTS S, simultaneous induction generates the proof obli- gations: (1) p(υ0 )a ndp(υ) ∧ q(υ) ⇒ p(υ � ), and (2) q(υ0 )a ndp(υ) ∧ q(υ) ⇒ q(υ � ) for each initial state υ0, each state υ and each successor state υ � of υ .I nstead, we may also use the proof obligations: (1) q(υ) ⇒ p(υ), and (2) q(υ0 )a ndp(υ) ∧ q(υ) ⇒ q(υ � ). The proof technique generating proof obligations like this is called semi-simultaneous induction. The proof obligation is equivalent to (1) q(υ) ⇒ p(υ), and (2) q(υ0 )a nd q(υ) ⇒ q(υ � ). But, the former may need less cases, making proofs shorter, than the latter. More importantly, the former makes it possible to record the process in which way lemmas have been conjectured. This article demonstrates some benefits of (semi- )simultaneous induction, describes semi-simultaneous induction and justifies it.

Testing Java implementations of algebraic specifications

In this paper we focus on exploiting a specification and the structures that satisfy it, to obtain a means of comparing implemented and expected behaviours and find the origin of faults in implementations. We present an approach to the creation of tests that are based on those specification-compliant structures, and to the interpretation of those tests' results leading to the discovery of the method responsible for an eventual test failure. Results of comparative experiments with a tool implementing this approach are presented.

Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal mu-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG), a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically.

Initial semantics in logics with constructors

The constructor-based logics constitute the logical foundation of the so-called OTS/CafeOBJ method, a modelling, specification and verification method of the observational transition systems. The important role played in algebraic specifications by the initial algebras semantics is well known. Free models along presentation morphisms provide semantics for the modules with initial denotation in structured specification languages. Following Goguen and Burstall, the notion of logical system over which we build specifications is formalized as an institution. The present work is an institution-independent study of the existence of free models along sufficient complete presentation morphisms in logics with constructors in the signatures.

Principles of proof scores in CafeOBJ

This paper describes the theoretical principles of a verification method with proof scores in the CafeOBJ algebraic specification language. The verification method focuses on specifications with conditional equations and realizes systematic theorem proving (or interactive verification). The method is explained using a simple but instructive example, and the necessary theoretical foundations, which justify every step of the verification, are described with precise mathematical definitions. Some important theorems that result from the definitions are also presented.

Semantic Observation Integration

Although the integration of sensor-based information into analysis and decision making has been a research topic for many years, semantic interoperability has not yet been reached. The advent of user-generated content for the geospatial domain, Volunteered Geographic Information (VGI), makes it even more difficult to establish semantic integration. This paper proposes a novel approach to integrating conventional sensor information and VGI, which is exploited in the context of detecting forest fires. In contrast to common logic-based semantic descriptions, we present a formal system using algebraic specifications to unambiguously describe the processing steps from natural phenomena to value-added information. A generic ontology of observations is extended and profiled for forest fire detection in order to illustrate how the sensing process, and transformations between heterogeneous sensing systems, can be represented as mathematical functions and grouped into abstract data types. We discuss the required ontological commitments and a possible generalization.

Category Theoretic Understandings of Universal Algebra and its Dual: Monads and Lawvere Theories, Comonads and What?

Universal algebra is often known within computer science in the guise of algebraic specification or equational logic. In 1963, it was given a category theoretic characterisation in terms of what are now called Lawvere theories. Unlike operations and equations, a Lawvere theory is uniquely determined by its category of models. Except for a caveat about nullary operations, the notion of Lawvere theory is equivalent to the universal algebraistʼs notion of an abstract clone. Lawvere theories were soon followed by a further characterisation of universal algebra in terms of monads, the latter quickly becoming preferred by category theorists but not by universal algebraists. In the 1990ʼs began a systematic attempt to dualise the situation. The notion of monad dualises to that of comonad, providing a framework for studying transition systems in particular. Constructs in universal algebra have begun to be dualised too, with different leading examples. But there is not yet a definitive dual of the concept of Lawvere theory, or that of abstract clone, or even a definitive dual of operations and equations. We explore the situation here.

Interaction protocols for cross-organisational workflows

Workflow technologies are widely used in industry and commerce to assist in the specification, execution and completion of well defined processes within organisations. As industrial and commercial relations have evolved, based on advances on information and communications technologies, cross-organisational workflow integration has become an important issue. Since organisations can have very different workflows, the creation of compatible workflows so that organisations can collaborate and/or carry out mutual transactions automatically in an integrated fashion can be a very complex and time consuming process. As a consequence, the development of technologies to support the creation and execution of compatible workflows is a most relevant issue. In the present article we introduce the JamSession coordination platform as a tool to implement cross-organisational workflow integration. JamSession is declarative and based on algebraic specification methods, and therefore workflow integration implemented using this platform can profit from formal behavioural analysis, based on which desired features and properties can be verified and/or obtained.

LeGESD: A framework oriented to the specification and formal validation of concurrent and distributed systems based on a graphical language and its process algebra semantics

The specification and formal verification of distributed systems is usually a complex task. It requires extensive knowledge of algorithm theory and modeling of distributed or concurrent systems. In this context, we present LeGESD which is a framework oriented to support the specification and formal validation of concurrent and distributed systems. LeGESD has a graphical formal language for the specification and analysis of distributed systems which is used to describe functional and of communication requirements. The semantics of LeGESD is based on the process algebra. This semantics is also described in this paper and it is called Analysis and Design of Distributed Systems (ADSD). ADSD is an algebraic specification with operational semantics defined to be used with LeGESD. ADSD provides graphical-algebraic equivalence relations which can be used to generate formal specifications of distributed systems. Lastly, this paper presents an example which shows the usefulness and potential of the language and its semantics.

Automatic equivalence proofs for non-deterministic coalgebras

A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analog of Kleene’s theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems covered include infinite streams, deterministic automata, Mealy machines and labeled transition systems. In this paper, we present a novel algorithm to decide whether two expressions are bisimilar or not. The procedure is implemented in the automatic theorem prover CIRC, by reducing coinduction to an entailment relation between an algebraic specification and an appropriate set of equations. We illustrate the generality of the tool with three examples: infinite streams of real numbers, Mealy machines and labeled transition systems.

Opening the black boxes in data flow optimization

Many systems for big data analytics employ a data flow abstraction to define parallel data processing tasks. In this setting, custom operations expressed as user-defined functions are very common. We address the problem of performing data flow optimization at this level of abstraction, where the semantics of operators are not known. Traditionally, query optimization is applied to queries with known algebraic semantics. In this work, we find that a handful of properties, rather than a full algebraic specification, suffice to establish reordering conditions for data processing operators. We show that these properties can be accurately estimated for black box operators by statically analyzing the general-purpose code of their user-defined functions. We design and implement an optimizer for parallel data flows that does not assume knowledge of semantics or algebraic properties of operators. Our evaluation confirms that the optimizer can apply common rewritings such as selection reordering, bushy join-order enumeration, and limited forms of aggregation push-down, hence yielding similar rewriting power as modern relational DBMS optimizers. Moreover, it can optimize the operator order of nonrelational data flows, a unique feature among today's systems.