Showing papers on "Formal language published in 2003"

Basic description logics

Abstract: This chapter provides an introduction to Description Logics as a formal language for representing knowledge and reasoning about it. It first gives a short overview of the ideas underlying Description Logics. Then it introduces syntax and semantics, covering the basic constructors that are used in systems or have been introduced in the literature, and the way these constructors can be used to build knowledge bases. Finally, it defines the typical inference problems, shows how they are interrelated, and describes different approaches for effectively solving these problems. Some of the topics that are only briefly mentioned in this chapter will be treated in more detail in subsequent chapters.

Fundamentals of control flow in workflows

Abstract: Although workflow management emerged as a research area well over a decade ago, little consensus has been reached as to what should be essential ingredients of a workflow specification language. As a result, the market is flooded with workflow management systems, based on different paradigms and using a large variety of concepts. The goal of this paper is to establish a formal foundation for control-flow aspects of workflow specification languages, that assists in understanding fundamental properties of such languages, in particular their expressive power. Workflow languages can be fully characterized in terms of the evaluation strategy they use, the concepts they support, and the syntactic restrictions they impose. A number of results pertaining to this classification will be proven. This should not only aid those developing workflow specifications in practice, but also those developing new workflow engines.

Networks of evolutionary processors

Abstract: In this paper we consider networks of evolutionary processors as language generating and computational devices. When the filters are regular languages one gets the computational power of Turing machines with networks of size at most six, depending on the underlying graph. When the filters are defined by random context conditions, we obtain an incomparability result with the families of regular and context-free languages. Despite their simplicity, we show how the latter networks might be used for solving an NP-complete problem, namely the “3-colorability problem”, in linear time and linear resources (nodes, symbols, rules).

Formal Modeling and Analysis of Software Architecture: Components, Connectors, and Events

Abstract: Developing a good software architecture for a complex system is a critically important step for insuring that the system will satisfy its principal objectives. Unfortunately, today descriptions of software architecture are largely based on informal “box-and-line” drawings that are often ambiguous, incomplete, inconsistent, and unanalyzable. This need not be the case. Over the past decade a number of researchers have developed formal languages and associated analysis tools for software architecture. In this paper I describe a number of the representative results from this body of work.

The mathematics of language

Abstract: This book studies language(s) and linguistic theories from a mathematical point of view. Starting with ideas already contained in Montague's work, it develops the mathematical foundations of present day linguistics. It equips the reader with all the background necessary to understand and evaluate theories as diverse as Montague Grammar, Categorial Grammar, HPSG and GB. The mathematical tools are mainly from universal algebra and logic, but no particular knowledge is presupposed beyond a certain mathematical sophistication that is in any case needed in order to fruitfully work within these theories. The presentation focuses on abstract mathematical structures and their computational properties, but plenty of examples from different natural languages are provided to illustrate the main concepts and results. In contrast to books devoted to so-called formal language theory, languages are seen here as semiotic systems, that is, as systems of signs. A language sign correlates form with meaning. Using the principle of compositionality it is possible to gain substantial insight into the interaction between form and meaning in natural languages.

A formal study of practical regular expressions

Abstract: Regular expressions are used in many practical applications. Practical regular expressions are commonly called "regex". It is known that regex are different from regular expressions. In this paper, we give regex a formal treatment. We make a distinction between regex and extended regex; while regex represent regular languages, extended regex represent a family of languages larger than regular languages. We prove a pumping lemma for the languages expressed by extended regex. We show that the languages represented by extended regex are incomparable with context-free languages and a proper subset of context-sensitive languages. Other properties of the languages represented by extended regex are also studied.

An algebraic approach to data languages and timed languages

Abstract: Algebra offers an elegant and powerful approach to understand regular languages and finite automata. Such framework has been notoriously lacking for timed languages and timed automata. We introduce the notion of monoid recognizability for data languages, which includes timed languages as special case, in a way that respects the spirit of the classical situation. We study closure properties and hierarchies in this model and prove that emptiness is decidable under natural hypotheses. Our class of recognizable languages properly includes many families of deterministic timed languages that have been proposed until now, and the same holds for non-deterministic versions.

Generating embedded software from hierarchical hybrid models

Abstract: Benefits of high-level modeling and analysis are significantly enhanced if code can be generated automatically from a model such that the correspondence between the model and the code is precisely understood. For embedded control software, hybrid systems is an appropriate modeling paradigm because it can be used to specify continuous dynamics as well as discrete switching between modes. Establishing a formal relationship between the mathematical semantics of a hybrid model and the actual executions of the corresponding code is particularly challenging due to sampling and switching errors. In this paper, we describe an approach to compile the modeling language Charon that allows hierarchical specifications of interacting hybrid systems. We show how to exploit the semantics of Charon to generate code from a model in a modular fashion, and identify sufficient conditions on the model that guarantee the absence of switching errors in the compiled code. The approach is illustrated by compiling a model for coordinated motion of legs for walking onto Sony's AIBO robot.

A universal approach to self-referential paradoxes, incompleteness and fixed points

Abstract: Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.

Abstract interpretation of programs as Markov decision processes

Abstract: We propose a formal language for the specification of trace properties of probabilistic, nondeterministic transition systems, encompassing the properties expressible in Linear Time Logic. Those formulas are in general undecidable on infinite deterministic transition systems and thus on infinite Markov decision processes. This language has both a semantics in terms of sets of traces, as well as another semantics in terms of measurable functions; we give and prove theorems linking the two semantics. We then apply abstract interpretation-based techniques to give upper bounds on the worst-case probability of the studied property. We propose an enhancement of this technique when the state space is partitioned -- for instance along the program points --, allowing the use of faster iteration methods.

Sticky-free and overhang-free DNA languages

Abstract: An essential step of any DNA computation is encoding the input data on single or double DNA strands. Due to the biochemical properties of DNA, complementary single strands can bind to one another forming double-stranded DNA. Consequently, data-encoding DNA strands can sometimes interact in undesirable ways when used in computations. It is crucial thus to analyze properties that guard against such phenomena and study sets of sequences that ensure that no unwanted bindings occur during any computation. This paper formalizes and investigates properties of DNA languages that guarantee their robusteness during computations. After defining and investigating several types of DNA languages possessing good encoding properties, such as sticky-free and overhang-free languages, we give algorithms for deciding whether regular DNA languages are invariant under bio-operations. We also give a method for constructing DNA languages that, in addition to being invariant and sticky-free, possess error-detecting properties. Finally, we present the results of running tests that check whether several known gene languages (the set of genes of a given organism) as well as the input DNA languages used in Adleman's DNA computing experiment, have the defined properties.

On the structural complexity of the motion description language MDLe

Abstract: As modern control theory attempts to elucidate the complexity of systems that combine differential equations and event-driven logic, it must overcome challenges having to do with limited expressive power as well as practical difficulties associated with translating control algorithms into robust and reusable software. The Motion Description Language (MDL) and its "extended" counterpart MDLe, have been at the center of an ongoing effort to make progress on both of these fronts. The goal of this paper is to define MDLe as a formal language, thereby connecting with the vast literature on the subject, and to stimulate experimental work. We discuss the expressive power of MDLe and provide some examples of MDLe programs.

Formal Semantics of Synchronous SystemC

Abstract: In this article, a denotational definition of a synchronous subset of SystemC is proposed. The subset treated includes modules, processes, threads, wait statement, ports and signals. We propose a formal model for SystemC delta delay. Also, we give a complete semantic definition for the language's two-phase scheduler. The proposed semantic can constitute a base for validating the equivalence of synchronous HDL subsets.

Verification of distributed object-based systems

Abstract: Distributed systems for open environments, like the Internet, are becoming more frequent and important. However, it is difficult to assure that such systems have the required functional properties. In this paper we use a visual formal specification language, called Object-Based Graph Grammars (OBGG), to specify asynchronous distributed systems. After discussing the main concepts of OBGG, we propose an approach for the verification of OBGG specifications using model checking. This approach consists on the translation of OBGG specifications into PROMELA (PROcess/PROtocol MEta LAnguage), which is the input language of the SPIN model checker. The approach we use for verification allows one to write properties based on the OBGG specification instead of on the generated PROMELA model.

Non-Standard Semantics for Program Slicing

Abstract: In this paper we generalize the notion of compositional semantics to cope with transfinite reductions of a transition system. Standard denotational and predicate transformer semantics, even though compositional, provide inadequate models for some known program manipulation techniques. We are interested in the systematic design of extended compositional semantics, observing possible transfinite computations, i.e. computations that may occur after a given number of infinite loops. This generalization is necessary to deal with program manipulation techniques modifying the termination status of programs, such as program slicing. We include the transfinite generalization of semantics in the hierarchy developed in 1997 by P. Cousot, where semantics at different levels of abstraction are related with each other by abstract interpretation. We prove that a specular hierarchy of non-standard semantics modeling transfinite computations of programs can be specified in such a way that the standard hierarchy can be derived by abstract interpretation. We prove that non-standard transfinite denotational and predicate transformer semantics can be both systematically derived as solutions of simple abstract domain equations involving the basic operation of reduced power of abstract domains. This allows us to prove the optimality of these semantics, i.e. they are the most abstract semantics in the hierarchy which are compositional and observe respectively the terminating and initial states of transfinite computations, providing an adequate mathematical model for program manipulation.

Using theoretical computer simulators for formal languages and automata theory

Abstract: Both formal languages and automata theory (FLAT) are core to the CS curricula but are difficult to teach and to learn. This situation has motivated the development of a number of theoretical computer simulators as educational tools to allow students to "bring to life" many topics that traditionally were presented only mathematically. This paper discusses the main features of software tools currently freely available via the Internet for teaching FLAT. Based on our practical experience, the tradeoffs between different FLAT software tools is analyzed and discussed. We conclude with general recommendations for integrating FLAT software tools into an established curriculum.

Flavor: A Language for Media Representation

Abstract: Flavor (Formal Language for Audio-Visual Object Representation) has been created as a language for describing coded multimedia bitstreams in a formal way so that the code for reading and writing bitstreams can be automatically generated. It is an extension of C++ and Java, in which the typing system incorporates bitstream representation semantics. This allows describing in a single place both the in-memory representation of data as well as their bitstream-level (compressed) representation. Flavor also comes with a translator that automatically generates standard C++ or Java code from the Flavor source code so that direct access to compressed multimedia information by application developers can be achieved with essentially zero programming. Flavor has gone through many enhancements and this paper fully describes the latest version of the language and the translator. The software has been made into an open source project as of Version 4.1, and the latest downloadable Flavor package is available at this http URL

Computing forbidden words of regular languages

Abstract: We give a quadratic-time algorithm to compute the set of minimal forbidden words of a factorial regular language. We give a linear-time algorithm to compute the minimal forbidden words of a finite set of words. This extends a previous result given for the case of a single word only. We also give quadratic-time algorithms to check whether a regular language is factorial or anti-factorial.

Formal Languages Arising from Gene Repeated Duplication

Abstract: We consider two types of languages defined by a string through iterative factor duplications, inspired by the process of tandem repeats production in the evolution of DNA. We investigate some decidability matters concerning the unbounded duplication languages and then fix the place of bounded duplication languages in the Chomsky hierarchy by showing that all these languages are context-free. We give some conditions for the non-regularity of these languages. Finally, we discuss some open problems and directions for further research.

Regular languages definable by Lindström quantifiers

Abstract: In our main result, we establish a formal connection between Lindstrom quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindstrom quantifiers associated with a class of regular languages.

Signed real measure of regular languages

Abstract: This paper reviews and extends the recent work on signed real measure of regular languages for discrete-event supervisory control within a unified framework. The language measure provides total ordering of any set of partially ordered sublanguages of a regular language to allow quantitative evaluation of the controlled behavior of deterministic finite state automata under different supervisors. The paper presents a procedure by which performance of different supervisors can be evaluated based on a common quantitative tool. Two algorithms are discussed for computation of the language measure. A physical interpretation of the language measure is given from the perspective of discrete-event supervisory control synthesis.

Testing membership in parenthesis languages

Abstract: We continue the investigation of properties defined by formal languages. This study was initiated by Alon et al. [1], who described an algorithm for testing properties defined by regular languages. Alon et al. also considered several context free languages, and in particular Dyck languages, which contain strings of properly balanced parentheses. They showed that the first Dyck language, which contains strings over a single type of pairs of parentheses, is testable in time independent of n, where n is the length of the input string. However, the second Dyck language, defined over two types of parentheses, requires Ω (log n) queries. Here we describe a sublinear-time algorithm for testing all Dyck languages. Specifically, the running time of our algorithm is O(n2/3/e3), where e is the given distance parameter. Furthermore, we improve the lower bound for testing Dyck languages to Ω (n1/11) for constant e. We also describe a testing algorithm for the context free language LREV = {uurvvr : u, v ∈ Σ*}, where Σ is a fixed alphabet. The running time of our algorithm is O(√n/e), which almost matches the lower bound given by Alon et al. [1].

On the power of tree-walking automata

Abstract: Tree-walking automata (TWAs) recently received new attention in the fields of formal languages and databases. To achieve a better understanding of their expressiveness, we characterize them in terms of transitive closure logic formulas in normal form. It is conjectured by Engelfriet and Hoogeboom that TWAs cannot define all regular tree languages, or equivalently, all of monadic second-order logic. We prove this conjecture for a restricted, but powerful, class of TWAs. In particular, we show that 1-bounded TWAs, that is TWAs that are only allowed to traverse every edge of the input tree at most once in every direction, cannot define all regular languages. We then extend this result to a class of TWAs that can simulate first-order logic (FO) and is capable of expressing properties not definable in FO extended with regular path expressions; the latter logic being a valid abstraction of current query languages for XML and semistructured data.