Showing papers on "Formal language published in 1994"

Finite Automata, Formal Logic, and Circuit Complexity

Abstract: Part 1 Mathematical preliminaries: words and languages automata and regular languages semigroups and homomorphisms. Part 2 Formal languages and formal logic: examples definitions. Part 3 Finite automata: monadic second-order sentences and regular languages regular numerical predicates infinite words and decidable theories. Part 4 Model-theoretic games: the Ehrenfeucht-Fraisse game application to FO [decreasing] application to FO [+1]. Part 5 Finite semigroups: the syntactic monoid calculation of the syntactic monoid application to FO [decreasing] semidirect products categories and path conditions pseudovarieties. Part 6 First-order logic: characterization of FO [decreasing] a hierarchy in FO [decreasing] another characterization of FO [+1] sentences with regular numerical predicates. Part 7 Modular quantifiers: definition and examples languages in (FO + MOD(P))[decreasing] languages in (FO + MOD)[+1] languages in (FO + MOD)[Reg] summary. Part 8 Circuit complexity: examples of circuits circuits and circuit complexity classes lower bounds. Part 9 Regular languages and circuit complexity: regular languages in NC1 formulas with arbitrary numerical predicates regular languages and non-regular numerical predicates special cases of the central conjecture. Appendices: proof of the Krohn-Rhodes theorem proofs of the category theorems.

Modeling and Control of Logical Discrete Event Systems

Abstract: Preface. 1. Introduction to Formal Language Theory. 2. Introduction to Lattice Theory. 3. Control under Complete Observation. 4. Control under Partial Observation. 5. Control of Non-Terminating Behavior. References. Index.

Supporting knowledge-base evolution with incremental formalization

Abstract: A number of systems have been built which integrate the knowledge representations of hypermedia and knowledge-based systems. Experiences with such have shown users are willing to use the semi-formal mechanisms of such systems systems leaving much structure implicit rather than use the formal mechanisms provided. The problem remains that it is hard (1) to encode knowledge in the formal languages required by knowledge-based systems and (2) to provide support with the semi-formal knowledge found in hypermedia systems. Incremental formalization enables users to enter information into the system in an informal or semi-formal representation and to have computer support for the formalization of this information. The domain independent Hyper-Object Substrate (HOS) differs from other systems that integrate hypermedia and knowledge-based system styles of representations in that it enables the incremental addition of formalism to any piece of information in the system. HOS actively supports incremental formalization with a set of tools which suggest new formalizations to be added to the information space. These suggestions are based on patterns in the informally and semi-formally represented information and the existing formalized knowledge in the information space. An important assumption is that suggestions need not be completely accurate to be of general benefit to users. These suggestions provide a starting point which can be edited, thus changing part of of formalization from creation to modification. XNetwork, an environment the process supporting the design of computer networks, is one of several applications that have been created with HOS. Experiences with HOS show that its flexibility for incrementally adding and formalizing information is useful for the rapid prototyping and modification of semi-formal information spaces.

Formal and computational aspects of natural language syntax

Abstract: This thesis explores issues related to using a restricted mathematical formalism as the formal basis for the representation of syntactic competence and the modeling of performance. The specific contribution of this thesis is to examine a language with considerably freer word-order than English, namely German, and to investigate the formal requirements that this syntactic freedom imposes. The formal systems investigated in this thesis are based on the tree adjoining grammar (TAG) formalism of Joshi et al. (1975). TAG is an appealing formalism for the representation of natural language syntax because its elementary structures are trees, which allows the linguist to localize linguistic dependencies such as agreement, subcategorization, and filler-gap relations, and to develop a theory of grammar based on the lexicon. The main results of the thesis are an argument that simple TAGs are formally inadequate, and the definition of an extension to TAG that is. Every aspect of the definition of this extension to TAG, called V-TAG, is specifically motivated by linguistic facts, not by formal considerations. A formal investigation of V-TAG reveals that (when lexicalized) it has restricted generative capacity, that it is polynomial parsable, and that it forms an abstract family of languages. This means that it has desirable formal properties for representing natural language syntax. Both a formal automaton and a parser for V-TAG are presented. As a consequence of the new system, a reformulation of the linguistic theory that has been proposed for TAG suggests itself. Instead of including a transformational step in the theory of grammar, all derivations are performed within mathematically defined formalisms, thus limiting the degrees of freedom in the linguistic theory, and making the theory more appealing from a computational point of view. The thesis sketches a fragment of a grammar of German, which covers phenomena such as scrambling, extraposition, topicalization, and the V2 effect. Finally, the formal automaton for V-TAG is used as a model of human syntactic processing. It is shown that this model makes several interesting predictions related to free word order in German.

A comparison of languages which operationalise and formalise {KADS} models of expertise

Abstract: In the field of Knowledge Engineering, dissatisfaction with the rapid-prototyping approach has led to a number of more principled methodologies for the construction of knowledgebased systems. Instead of immediately implementing the gathered and interpreted knowledge in a given implementation formalism according to the rapid-prototyping approac h, many such methodologies centre around the notion of a conceptual model: an abstract, implementation independent description of the relevant problem solving expertise . A conceptual model should describe the task which is solved by the system and the knowledge which is required by it. Although such conceptual models have often been formulated in an informal way, recent years have seen the advent of formal and operational languages to describe such conceptual models more precisely, and operationally as a means for model evaluation. In this paper, we study a number of such formal and operational languages for specifying conceptual models. In order to enable a meaningful comparison of such languages, we focus on languages which are all aimed at the same underlying conceptual model, namely that from the KADS method for building KBS. We describe eight formal languages for KADS models of expertise, and compare these languages with respect to their modelling primitives, their semantics, their implementations and their applications. Future research issues in the area of formal and operational specification languages for KBS are identified as the result of studying thes e languages. The paper also contains an extensive bibliography of research in this area.

Blocking and controllability of Petri nets in supervisory control

Abstract: This note discusses the use of Petri net languages in supervisory control theory. First it is shown that the trimming of an unbounded Petri net is not always possible and a new class of Petri net languages, that may be generated by nonblocking nets, is defined. Secondly, necessary and sufficient conditions for the existence of a Petri net supervisor, under the hypothesis that the system's behavior and the legal behavior are both Petri net languages, are derived. Finally, by means of an example, it is shown that Petri net languages are not closed under the supremal controllable sublanguage operator. >

Formal syntax and semantics of programming languages

Abstract: This text developed out of our experiences teaching courses covering the formal semantics of programming languages

Supervision of Infinite Behavior of Discrete-Event Systems

Abstract: Some basic results of supervisory control theory are extended to the setting of $\omega$-languages, formal languages consisting of infinite strings. The extension permits the investigation of both liveness and safety issues in the control of discrete-event systems. A new controllability property appropriate to the infinitary setting ($\omega$-controllability) is defined; this language property captures in a natural way the limitations of available control actions. It is shown that every specification language contains a unique maximal $\omega$-controllable sublanguage, representing the least upper bound of the set of achievable closed-loop sublanguages. This supremal $\omega$-controllable sublanguage allows a simple formulation of necessary and sufficient conditions for the solvability of an infinitary supervisory control problem. The problems of effectively deciding solvability of the control problem and of effectively synthesizing appropriate supervisors are solved for the case where the plant is represented by a deterministic Buchi automaton and the specification of legal behavior by a deterministic Rabin automaton.

A typed logic of partial functions reconstructed classically

Abstract: This paper gives a comprehensive description of a typed version of the logic known as LPF. This logic is basic to formal specification and verified design in the software development method VDM. If appropriately extended to deal with recursively defined functions, the data types used in VDM, etc., it gives the VDM notation and its associated rules of reasoning. The paper provides an overview of the needed extensions and examines some of them in detail. It is shown how this nonclassical logic-and the extensions-can be reconstructed classically by embeddings into classical infinitary logic.

From English to formal specifications

Abstract: Specifications provide the foundation upon which a system can be formally developed. If a specification is wrong, then no matter what method of design is used, or what quality assurance procedures are in place, they will not result in a system that meets the requirements. The specification of a system involves people of different profiles who favour different representations. At the beginning natural language is used because the specification document acts as a contract between the user and the developers. Most of the time, the only representation that users understand and agree on is natural language. At the other end, developers find natural language specifications ambiguous and incomplete and may therefore prefer formal specifications. The transition from informal specifications to formal ones is an error prone and time consuming process. This transition must be supported to ensure that the formal specifications are consistent with the informal ones. In this research we propose an interactive approach for producing formal specifications from English specifications. The approach uses research in the area of natural language understanding to analyse English specifications in order to detect ambiguities. The method used for analysing natural language text is based on McCord’s approach. This method consists of translating natural language sentences into a logical form language representation. This helps to identify ambiguities present in natural language specifications and to identify the entities and relationships. These entities and relationships are used as a basis for producing VDM data types. We also investigate the production of data type invariants for restricted sentences and the production of some common specifications. We test our approach by implementing it in Prolog-2 and apply it to an independent case study.

Pattern languages with and without erasing

Abstract: The paper deals with the problems related to finding a pattern common to all words in a given set We restrict our attention to patterns expressible by the use of variables ranging over words Two essentially different cases result, depending on whether or not the empty word belongs to the range We investigate equivalence and inclusion problems, patterns descriptive for a set, as well as some complexity issues The inclusion problem between two pattern languages turns out to be of fundamental theoretical importance because many problems in the classical combinatorics of words can be reduced to it

Variable lookahead supervisory control with state information

Abstract: In cases where the discrete-event system model has an infinite or large state space, or when it is not completely specified a priori, applying the traditional off-line methods for computing the control policy may be impractical, if not infeasible. We adopt an online limited lookahead approach. Under this approach, the next control action is determined based on an N-step ahead projection of the system behavior and on one of two attitudes-conservative or optimistic. We extend this approach to incorporate knowledge of the system state in the computation. This has the potential of improving the efficiency of the computation as well as the quality of the control policy. There are five specific contributions presented in this paper: 1) a new algorithm for the online computation of supervisory controls with worst case complexity that is quadratic in the number of "expanded" states, 2) an algorithmic proof of the correctness of this algorithm that avoids using fixed point methods and offers new insight into the structure of the supremal controllable sublanguage, 3) an off-line version based on a forward search technique that has the same worst case complexity as existing off-line algorithms but is potentially more efficient, 4) a formal proof of the fact that when the languages of interest are livelock free the computations are performed in linear complexity, and 5) new bounds on the depth of the lookahead window that guarantee optimality. >

Formal languages and infinite groups.

Abstract: This article is an introduction to formal languages from the point of view of combinatorial group theory.

A Computational Account for a Description Logic of Time and Action

Abstract: A formal language for representing and reasoning about time and action is presented. We employ an action representation in the style of Allen, where an action is represented by describing the time course of events while the action occurs. In this sense, an action is defined by means of temporal constraints on the world states, which pertain to the action itself, and on other more elementary actions occurring over time. A distinction between action types and individual actions is supported by the formalism. Plans are seen as complex actions whose properties possibly change with time. The formal representation language used in this paper is a description logic, and it is provided with a well founded syntax, semantics and calculus. Algorithms for the subsumption and recognition tasks - forming the basis for action management - are provided.

Regular language induction with genetic programming

Abstract: In this research, inductive inference is done with an informant on the class of regular languages. The approach is to evolve formal language accepters which are consistent with a set of sample strings from the language, and a set of sample strings known not to be in the language. Deterministic finite automata (DFA) were chosen as the formal language accepters to alleviate the computational difficulties of nondeterministic constructs such as rewrite grammars. Genetic programming (GP) offers two significant improvements for regular language induction over genetic algorithms. First, GP allows the size of the solution (the DFA) to be determined at run time in response to population pressure. Second, GP's potential for assuring correct dependencies in complex individuals can be exploited to assure that all states in a DFA are reachable from the start state. The contribution of this research is the effective translation of DFAs to S-expressions, the application of renumbering, and of editing to the problem of language induction. DFAs or transition tables form the basis of many problems. By using the techniques found in this paper, many of these problems can be directly translated into the domain of genetic programming. >

The Language of Machines: an Introduction to Computability and Formal Languages

Abstract: An up-to-date, authoritative text for courses in theory of computability and languages. The authors redefine the building blocks of automata theory by offering a single unified model encompassing all traditional types of computing machines and "real world" electronic computers. This reformulation of computablity and formal language theory provides a framework for building a body of knowledge. A solutions manual and an instructor's software disk are also available.

A predictive parser for visual languages specified by relation grammars

Abstract: We define a class of relation grammars that satisfy the context-freeness property, which is an essential condition to solve the membership problem in polynomial time. The context-freeness property is used to design a predictive parsing algorithm for such grammars. The algorithm has a polynomial time behaviour when applied to grammars which generate languages having the additional properties of connections and degree-boundedness. One remarkable result is that a polynomial time complexity is obtained without imposing (total or partial) ordering on the symbols of input sentences. >

Translations of network languages

Abstract: In this paper, we describe new results of research on geometrical properties of complex control systems, the so-called Linguistic Geometry. This research includes the development of syntactic tools for knowledge representation and reasoning about large-scale hierarchical complex systems. It relies on the formalization of search heuristics of high-skilled human experts that have resulted in the development of successful applications in different areas. A hierarchy of subsystems of a complex system, the networks of paths, is represented as a hierarchy of formal languages. In this paper, we investigate transformations of these networks while a system moves from one state to another. The investigation consists of formal, constructive separation of changed and unchanged parts of system representation, the hierarchy of languages. Thus, we address a problem relative to the well-known Frame Problem for planning systems. A partial solution is presented in the form of the theorem about translations of network languages. Formal considerations are illustrated by example of Air Force robotic vehicles.

A formal framework for ASTRAL intralevel proof obligations

Abstract: ASTRAL is a formal specification language for real-time systems. It is intended to support formal software development, and therefore has been formally defined. This paper focuses on how to formally prove the mathematical correctness of ASTRAL specifications. ASTRAL is provided with structuring mechanisms that allow one to build modularized specifications of complex systems with layering. In this paper, further details of the ASTRAL environment components and the critical requirements components, which were not fully developed in previous papers, are presented. Formal proofs in ASTRAL can be divided into two categories: interlevel proofs and intralevel proofs. The former deal with proving that the specification of level i+1 is consistent with the specification of level i, and the latter deal with proving that the specification of level i is consistent and satisfies the stated critical requirements. This paper concentrates on intralevel proofs. >

Generating formal cryptographic protocol specifications

Abstract: This paper describes a tool which translates a cryptographic protocol specified in the semi-formal standard notation i. A/spl rarr/B:M into the formal language CKT5. We examine the standard notation syntax, and describe how it is exploited by the tool to infer protocol conditions which must hold for every principal, thereby obtaining a complete, formal specification of the protocol. The translation criteria described herein are applicable to other target languages than CKT5. >

On the reachability and reversibility problems in a class of Petri nets

Abstract: The paper faces the reachability and the reversibility problems in a class of Petri nets larger than other classes investigated for the same problems. The considered class of Petri net represents a formal language to design and analyze logic controllers. These nets may be decomposed in simple structures, called elementary control tasks, linked together through a limited number of connections, giving rise to arbitrarily complex nets. Such connections are the ones encountered in a typical logic control problem, as exchange of enabling signals (consensus/deny to control maneuvers) and the synchronous execution (shared resources modeling or shared operations). The purpose of the paper is to enlarge the set of theoretical tools previously developed for the incremental approach to the liveness analysis of a net, to be incorporated into a special CAD environment. In particular, the addressed topics are the choice of the initial marking and the analysis of reachability of nonlive markings. >

Language driven hybrid systems

Abstract: In this paper the author shows how the type of hybrid models introduced previously by him (1993) can be used to evaluate the performance of motion control systems. He defines an appropriate class of formal languages, allowing one to frame such problems succinctly as word-to-position transducers. We show that models involving multiple triggers play an important role in modeling this type of motion control system. >

Valuations and Unambiguity of Languages, with Applications to Fractal Geometry

Abstract: Valuations — morphisms from (Σ*·λ) to ((0, ∞),·,1) —are a simple generalization of Bernoulli morphisms (distributions, measures) as introduced in [12, 20, 6, 4, 5, 21]. This paper shows that valuations are not only useful within the theory of codes, but also when dealing with ambiguity, especially in regular expressions and contextfree grammars, or for defining outer measures on the space of ω-words which are of some importance for the theory of fractals. These connections yield new formulae to determine the Hausdorff dimension of fractal sets (especially in Euclidean spaces) defined via regular expressions and contextfree grammars.

Recognizing substrings of LR(k) languages in linear time

Abstract: LR parsing techniques have long been studied as being efficient and powerful methods for processing context-free languages. A linear-time algorithm for recognizing languages representable by LR(k) grammars has long been known. Recognizing substrings of a context-free language is at least as hard as recognizing full strings of the language, since the latter problem easily reduces to the former. In this article we present a linear-time algorithm for recognizing substrings of LR(k) languages, thus showing that the substring recognition problem for these languages is no harder than the full string recognition problem. An interesting data structure, the Forest-Structured Stack, allows the algorithm to track all possible parses of a substring without loosing the efficiency of the original LR parser. We present the algorithm, prove its correctness, analyze its complexity, and mention several applications that have been constructed.