Showing papers on "Formal language published in 1986"
TL;DR: This paper extracts a single hybrid approach having a rich language that mixes algebra and logic and having a natural class of models of concurrent processes, a notion of partial string derived from the view of a string as a linearly ordered multiset by relaxing the linearity constraint, thereby permitting partially ordering multisets or pomsets.
Abstract: Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic,inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a natural class of models of concurrent processes. The heart of the approach is a notion of partial string derived from the view of a string as a linearly ordered multiset by relaxing the linearity constraint, thereby permitting partially ordered multisets orpomsets. Just as sets of strings form languages, so do sets of pomsets form processes. We introduce a number of operations useful for specifying concurrent processes and demonstrate their utility on some basic examples. Although none of the operations is particularly oriented to nets it is nevertheless possible to use them to express processes constructed as a net of subprocesses, and more generally as a system consisting of components. The general benefits of the approach are that it is conceptually straightforward, involves fewer artificial constructs than many competing models of concurrency, yet is applicable to a considerably wider range of types of systems, including systems with buses and ethernets, analog systems, and real-time systems.
658 citations
Book•
01 Jan 1986TL;DR: In this article, a deductive belief model based on the notion of deduction is proposed to represent and reason about the knowledge an agent (human or computer) must have to accomplish some task.
Abstract: Representing and reasoning about the knowledge an agent (human or computer) must have to accomplish some task is becoming an increasingly important issue in artificial intelligence (AI) research. To reason about an agent's beliefs, an AI system must assume some formal model of those beliefs. An attractive candidate is the Deductive Belief model: an agent's beliefs are described as a set of sentences in some formal language (the base sentences), together with a deductive process for deriving consequences of those beliefs. In particular, a Deductive Belief model can account for the effect of resource limitations on deriving consequences of the base set: an agent need not believe all the logical consequences of his beliefs. In this paper we develop a belief model based on the notion of deduction, and contrast it with current AI formalisms for belief derived from Hintikka/Kripke possible-worlds semantics for knowledge.
425 citations
TL;DR: In this paper, the authors contrast the interpreted-symbolic-structure approach and situated-automata approach, which seeks to analyze knowledge in terms of relations between the state of a machine and its environment over time using logic as a metalanguage in which the analysis is carried out.
Abstract: Although the concept ofknowledge plays a central role in artificial intelligence, the theoretical foundations of knowledge representation currently rest on a very limited conception of what it means for a machine to know a proposition. In the current view, the machine is regarded as knowing a fact if its state either explicitly encodes the fact as a sentence of an interpreted formal language or if such a sentence can be derived from other encoded sentences according to the rules of an appropriate logical system. We contrast this conception, the interpreted-symbolic-structure approach, with another, the situated-automata approach, which seeks to analyze knowledge in terms of relations between the state of a machine and the state of its environment over time using logic as a metalanguage in which the analysis is carried out.
162 citations
TL;DR: RT-ASLAN as mentioned in this paper is an extension of the ASLAN specification language for sequential systems that supports specification of parallel real-time processes through arbitrary levels of abstraction; processes do not have to be specified to the same level of detail.
Abstract: RT-ASLAN, a formal language for specifying real-time systems, is an extension of the ASLAN specification language for sequential systems. Some of the features of the ASLAN language, such as constructs for writing procedural semantics in a nonprocedural logical language, are highlighted. The RT-ASLAN language supports specification of parallel real-time processes through arbitrary levels of abstraction; processes do not have to be specified to the same level of detail. Communicating processes use an interface process as an abstract data type representing shared information. From RT-ASLAN specifications, performance correctness conjectures are generated. These conjectures are logic statements whose proof guarantees that the specification meets critical time bounds. A detailed example as well as a discussion of the advantages and disadvantages of formal specification and verification are included.
92 citations
TL;DR: It is shown that it is decidable whether an infinité word gênerated by iterated morphism is ultimately periodic or not.
Abstract: — We show that it is decidable whether an infinité word gênerated by iterated morphism is ultimately periodic or not. Résumé. — Nous montrons qu'on peut décider si un mot infini engendré par morphisme itéré est uitimement périodique.
79 citations
TL;DR: By viewing level- n grammars as modeling recursive procedures on higher types the iterated pushdown automation thus provides an operational model for the run-time behavior of procedures defined by recursion on higher type which makes the results of this paper interesting not only from a language theoretical point of view.
Abstract: This paper gives an automata-theoretical characterization of the OI-hierarchy ( Damm (1982) , Engelfriet and Schmidt (1977) , Wand (1975) ). This hierarchy is generated by so-called level- n grammars which are natural generalizations from context free and macro grammars in that their nonterminals are treated as functionals of higher type, i.e., they are allowed to carry up to n levels of parameters. The automata model used for this characterization is the n -iterated pushdown automaton. Its characteristic feature is the storage structure which consists of a nesting of pushdowns up to nesting depth n . The equivalence proof is given constructively, its method is illustrated using examples. By viewing level- n grammars as modeling recursive procedures on higher types the iterated pushdown automation thus provides an operational model for the run-time behavior of procedures defined by recursion on higher types which makes the results of this paper interesting not only from a language theoretical point of view.
73 citations
08 Sep 1986
TL;DR: In this article, the authors present a survey of the many applications of the theory of parallel algorithms and complexity to logic programming problems, including query optimization for deductive databases and fast parallel execution of primitive operations in logic programming languages, such as fixpoint operators, term unification, and term matching.
Abstract: This paper is a survey of the many applications of the theory of parallel algorithms and complexity to logic programming problems. The mathematical tools relevant to the analysis of parallel logic programs include: the concept of alternation, the complexity class NC, and parallel algorithms using randomization and/or achieving optimal speed-ups. The logic programming problems addressed are related to query optimization for deductive databases and to fast parallel execution of primitive operations in logic programming languages, such as, fixpoint operators, term unification, and term matching. The formal language we use to illustrate the addition of recursion to database queries is the language of logical query programs (or programs), whose evaluation has been the object of much recent research. Our presentation highlights the fact that all of these results can be stated using the stage function sH(n) of a program H, where n is the size of the database queried. In this context we also present two new observations. (1) Given a linear single rule program H, it is NP-hard to decide whether sH(n)=O(1); this extends the bounded recursion analysis of[57, 42]. (2) There is a program that can be evaluated in s(n)=O(log n) stages, but whose derivation trees (of width 1) are of size exponential in n. An extension of derivation trees from width 1 to constant width properly strengthens the fast evaluation method of [76].
68 citations
08 Sep 1986
TL;DR: In this article, the authors define families of formal languages related to classes of P/T-systems and define transition sequences as a way to define the possible finite or infinite occurence sequences of a Petri net to the transitions.
Abstract: Petri nets where multiple arcs are allows and the capacity of the places need not be bounded are here called Place/Transition systems. The restrictions of the possible finite or infinite occurence sequences of a P/T-system to the transitions are called transition sequences and give the basis to define families of formal languages related to classes of P/T-systems.
53 citations
TL;DR: The Vienna development method (VDM), a formal specification and development methodology, was used during the analysis phase of the assessment of a prototype nuclear reactor protection system and was translated into the logic language Prolog to animate the specification.
Abstract: A case study is presented in which the Vienna development method (VDM), a formal specification and development methodology, was used during the analysis phase of the assessment of a prototype nuclear reactor protection system. The VDM specification was also translated into the logic language Prolog to animate the specification and to provide a diverse implementation for use in back-to-back testing. It is claimed that this technique provides a visible and effective method of analysis which is superior to the informal alternatives.
52 citations
01 Oct 1986
TL;DR: In this article, a temporal logic extended with two modalities that can be used to support planning in temporally rich domains is presented, in particular planning environments that have assertions about future possibilities in addition to the present state, and plans that contain concurrent actions.
Abstract: This paper outlines a temporal logic extended with two modalities that can be used to support planning in temporally rich domains. In particular, the logic can represent planning environments that have assertions about future possibilities in addition to the present state, and plans that contain concurrent actions. The logic is particularly expressive in the ways that concurrent actions can interact with each other and allows situations where either one of the actions can be executed, but both cannot, as well as situations where neither action can be executed alone, but they can be done together. Two modalities are introduced and given a formal semantics: INEV expresses simple temporal possibility, and IFTRIED expresses counteffactual-like statements about actions.
TL;DR: The purpose of this paper is to call attention to the powerful dormant tools that can be used in the design arts and some of the benefits of using these tools for describing existing (natural) design languages are discussed.
Abstract: Although substantial literature exists on the properties of formal grammars, much less has been written on the use of grammars for describing the languages which they are capable of explaining. Thus we see a well-developed theory concerning the expressive (generative) power of different kinds of formal grammars and powerful algorithmic methods (analytical) for the languages defined by these grammars. For natural spoken and written languages, grammars have been used for explaining their structure but for the two-dimensional generalization to designs, pictures, images, and fine arts, which has been known since 1964, almost no use has been made of grammars.The purpose of this paper is to call attention to the powerful dormant tools that can be used in the design arts. Some of the benefits of using these tools for describing existing (natural) design languages are discussed. How such uses may direct us from the more formal design arts into the fine arts is discussed by reporting progress on building a grammar...
15 Jul 1986
TL;DR: An effective criterion for determining whether a given language has dot-depth 2 is conjecture and the condition is shown to be necessary in general, and sufficient for languages over a two-letter alphabet.
Abstract: This paper is a contribution to the problem of effectively determining the dot-depth of a star-free language, a problem in the theory of automata and formal languages with close connections to algebra and formal logic. We conjecture an effective criterion for determining whether a given language has dot-depth 2. The condition is shown to be necessary in general, and sufficient for languages over a two-letter alphabet. The condition involves a novel use of categories in the study of semigroup-theoretic problems.
TL;DR: Using this resuit, a number of decidability results and characterizations of closure properties for the three above mentioned families of trace languages are derived.
Abstract: A concurrent alphabet is a pair <£= <£, C>, where I is an alphabet and C is a relation over £, called the concurrency relation. Two words over Z are called C-equivalent, if they can be obtained from each other by successively interchanging adjacent symbols which are related by C. A trace (over <$) is now simply an équivalence class with respect to C-equivalence. This paper considers trace languages (i. e., sets of traces) as they are deflned by regular string languages in the following ways: (i) existentially regular trace languages (the trace language defined existentially by a regular string language L consists of ail traces which have a représentative in L), (ii) universally regular trace languages (the trace language defined universally by a regular string language L consists of ail traces which have all représentatives in L), and (iii) consistently regular trace languages (a regular string language L defines a consistently regular trace language T if and only if L is the union of all the traces in T). In particular, the main resuit of this paper characterizes those concurrent alphabets for which the family of existentially regular trace languages equals the family of universally regular trace languages. Furthermore, using this resuit, a number of decidability results and characterizations of closure properties for the three above mentioned families of trace languages are derived. Résumé. Un alphabet concurrent est un couple ̂ —<£, *C>, où £ est un alphabet et C est une relation sur E, appelée relation de concurrence. Deux mots sur Valphabet S sont dits C-équivalents, s'ils peuvent se déduire Vun de Vautre par interversions successives de symboles adjacents en relation par C. Une trace (sur #) est une classe d'équivalence par rapport à la C-équivalence. Dans cet article, on considère des langages de trace comme étant des langages réguliers définis de diverses façons : (i) langages de trace réguliers existentiels (le langage de trace défini « existentiellement » par un langage régulier L est constitué de toutes les traces ayant un représentant dans L), (ii) langages de trace réguliers universels (le langage de trace défini « universellement » par un langage régulier est constitué de toutes les traces qui ont tous leurs représentants dans L)t (iii) langages de trace réguliers consistent (un langage régulier L définit un langage de trace régulier et consistent T si et seulement si L est l'union de toutes les traces dans T). En particulier, le résultat principal de cet article caractérise les alphabets concurrents pour lesquels la famille des langages de trace réguliers existentiels est égal à la famille des langages de trace réguliers universels. De plus, en utilisant ce résultat, on obtient divers résultats de décidabilité et des caractérisations des propriétés de clôtures relatives aux trois familles mentionnées ci-dessus. (*) Received in October 1984, revised in June 1985. () Institute of .Applied Mathematics and Computer Science, University of Leiden, Wassenaarseweg 80, Leiden, The Netherlands. () Institute of Applied Mathematics and Computer Science, University of Leiden, Wassenaarseweg 80, Leiden, The Netherlands. On leave from: Institutes for Information Processing, IIG, Technical University of Graz and Austrian Computer Society, Schiessstattgasse 4a, A-8010 Graz, Austria. informatique théorique et Applications/Theoretical Informaties and Applications 0296-1598/86/02103 17/S3.70/© Gauthier-Villars 104 IJ. J. AALBERSBERG, E. WELZL
TL;DR: The possibility of executing a language's semantic description directly supports a methodology of language design that is advocate: express the design as a formal language description, and use this to test and refine the design, before becoming committed to constructing a compiler.
Abstract: We describe how the denotational semantics of a programming language can be executed directly, if it is expressed in a suitable functional programming language such as ML. We also apply Mosses' idea of ‘semantic algebras’ to construct semantic descriptions that are significantly more modular and understandable than usual. The possibility of executing a language's semantic description directly supports a methodology of language design that we advocate: express the design as a formal language description, and use this to test and refine the design, before becoming committed to constructing a compiler.
TL;DR: It is shown that the output language (i.e., the range of the translation) of a SAG is log-space reducible to a context-free language.
Abstract: A string-valued attribute grammar (SAG) has a semantic domain of strings over some alphabet, with concatenation as basic operation. It is shown that the output language (i.e., the range of the translation) of a SAG is log-space reducible to a context-free language.
01 Jan 1986
TL;DR: Despite its firm basis in theoretical biology, L systems theory has had some far reaching repercussions in mathematics and theoretical computer science as mentioned in this paper, one of these is the emphasis on iterated composition of morphisms on a free monoid (word morphisms).
Abstract: Despite its firm basis in theoretical biology L systems theory has had some far reaching repercussions in mathematics and theoretical computer science. One of these is the emphasis on iterated composition of morphisms on a free monoid (word morphisms). This leads naturally to set equivalence problems, familiar from formal language theory, and sequence equivalence problems (variously known also as strong equivalence, graph equivalence or tree equivalence problems in deterministic L systems theory).
TL;DR: An algorithm which computes the set of descendants of a regular set R, for Thue systems of certain type is given, which allows to improve the known complexity bounds for some extended word problems defined by cancellation rules.
10 Jul 1986
TL;DR: The absence of mirror-image constructions in human languages means that it is not enough to extend Context-free Grammars in the direction of context-sensitivity, and a class of grammars must be found which handles (context-sensitive) copying but not ( context-free) mirror images, suggesting that human linguistic processes use queues rather than stacks.
Abstract: The documentation of (unbounded-length) copying and cross-serial constructions in a few languages in the recent literature is usually taken to mean that natural languages are slightly context-sensitive. However, this ignores those copying constructions which, while productive, cannot be easily shown to apply to infinite sublanguages. To allow such finite copying constructions to be taken into account in formal modeling, it is necessary to recognize that natural languages cannot be realistically represented by formal languages of the usual sort. Rather, they must be modeled as families of formal languages or as formal languages with indefinite vocabularies. Once this is done, we see copying as a truly pervasive and fundamental process in human language. Furthermore, the absence of mirror-image constructions in human languages means that it is not enough to extend Context-free Grammars in the direction of context-sensitivity. Instead, a class of grammars must be found which handles (context-sensitive) copying but not (context-free) mirror images. This suggests that human linguistic processes use queues rather than stacks, making imperative the development of a hierarchy of Queue Grammars as a counterweight to the Chomsky Grammars. A simple class of Context-free Queue Grammars is introduced and discussed.
TL;DR: This work investigates a trace-set semantics of processes with ?
01 Jan 1986
TL;DR: An algorithm for incremental semantic analysis is presented, which guarantees immediate detection of semantic errors even in arbitrary incomplete program fragments, generated from the language's context conditions, which are described by inference rules.
Abstract: Language-specific editors for typed programming languages must contain a subsystem for semantic analysis in order to guarantee correctness of programs with respect to the context conditions of the language. As programs are usually incomplete during development, the semantic analysis must be able to cope with missing context information, e. g. incomplete variable declarations or calls to procedures imported from still missing modules. In this paper we present an algorithm for incremental semantic analysis, which guarantees immediate detection of semantic errors even in arbitrary incomplete program fragments. The algorithm is generated from the language's context conditions, which are described by inference rules. During editing, these rules are evaluated using a unification algorithm for many-sorted algebras with semi-lattice ordered subsorts and non-empty equational theories. The method has been implemented as part of the PSG system, which generates interactive programming environments from formal language definitions, and has been successfully used to generate an incremental semantic analysis for PASCAL and MODULA-2.
TL;DR: In this paper the axiomatization of the elementary laws of genetics considered in Rizzotti & Zanardo (1986) is translated into a formal language and an axiomatic theory is defined in which the (translated) laws are deducible.
TL;DR: It is proved that one can decide whether Rω is finitely generated, that is, whether R ω = Fω for some finite set F.
02 Dec 1986
TL;DR: A new model, based in the graph grammars, that manipulates the bounding manifolds of physical solids, that guarantees topological correctness of computer representations of physicalsolids is outlined.
Abstract: Linguistic models of physical solids have been widely studied for use in the kernels of CAD/CAM systems. These models are useful because they guarantee topological correctness of computer representations of physical solids. This papers outlines a new model, based in the graph grammars, that manipulates the bounding manifolds of physical solids. Proof of topological validity of this linguistic representation scheme proceeds as follows. First, the start graph is shown to be representative of a solid, then productions in the two dimensional grammar are shown to be syntactically complete and closed in the solids. Thus one starts with a solid topology, and any application of a graph production results in a solid topology.
TL;DR: The main results are the following: (i) the equivalence problem of inverses of finite substitutions on regular languages is undecidable, (ii) the existential equivalence problems of finite substitution on regular language is undECidable, and (iii) the length-equivalences problem of finite substituted languages is decidable.
Abstract: Equivalence problems of some transductions involving letter to letter morphisms on regular languages are discussed. In particular, we deal with finite substitutions and inverses of finite substitutions. Our main results are the following: (i) The equivalence problem of inverses of finite substitutions on regular languages is undecidable, (ii) The existential equivalence problem of finite substitutions on regular languages is undecidable, and (iii) The length-equivalence problem of finite substitutions on regular languages is decidable.
Book•
01 Jan 1986
TL;DR: A new and revised edition of this innovative introductory logic textbook explores the relationship between natural language and logic, motivating the student to acquire skills and techniques of formal logic.
Abstract: Book synopsis: With the same intellectual goals as the first edition, this innovative introductory logic textbook explores the relationship between natural language and logic, motivating the student to acquire skills and techniques of formal logic. This new and revised edition includes substantial additions which make the text even more useful to students and instructors alike. Central to these changes is an Appendix, 'How to Learn Logic', which takes the student through fourteen compact and sharply directed lessons with exercises and answers.
TL;DR: Within the framework of these generalized expressions the task of the inductive synthesis of programs from its sample run is formalized and special automata recognizing the sets defined by generalized expressions are introduced, and their equivalence problem is shown to be recursively solvable.
TL;DR: Deterministic chains of push-down transducers are introduced as a model of multi-pass compilers and the family is a strict hierarchy ordered by the length of the chain, which strictly includes the Boolean closure of deterministic languages.
Abstract: Chains (or cascade composition) of push-down transducers are introduced as a model of multi-pass compilers. We focus on deterministic chains, since nondeterministic transducer chains of length two define the recursively enumerable sets. Deterministic chains recognize in linear time a superset of context-free deterministic languages. This family is $\mathcal{CH}$ closed under Boolean operations, disjoint shuffle,and reverse deterministic pushdown translation, but not under homomorphism. Equivalent definitions of the family in terms of composition of syntax-directed translation schemes and control languages are considered. The family is a strict hierarchy ordered by the length of the chain. The complexity of $\mathcal{CH}$ is obviously linear, but not all linear-time parsable languages are in $\mathcal{CH}$. On the other hand it strictly includes the Boolean closure of deterministic languages. Finally $\mathcal{CH}$ is not comparable with another classical Boolean algebra of formal languages, namely real-ti...
TL;DR: To show the practical feasibility of attribute grammar inversion, experience in inverting an attribute grammar used as an interface for a formal database accessing language, SQL, is related; the attributed grammar is used to paraphrase SQL database queries in English.
Abstract: Attribute grammars constitute a formal mechanism for specifying translations between languages; from a formal description of the translation, a translator can be automatically constructed. This process is taken one step further; given an attribute grammar specifying the translation from language L1 to language L2, the question of whether the inverse attribute grammar specifying the inverse translation from L2 to L1 can be automatically generated is addressed. It is shown how to solve this problem for a restricted subset of attribute grammars. This inversion process allows compatible two-way translators to be generated from a single description. To show the practical feasibility of attribute grammar inversion, experience in inverting an attribute grammar used as an interface for a formal database accessing language, SQL, is related. The attributed grammar is used to paraphrase SQL database queries in English.