Ambiguity in context free languages
TL;DR: It is shown that no language contained in w, each of which contains w, is inherently ambiguous, and a necessary and sufficient algebraic condition is given for a bounded language to be inherently ambiguous.
Abstract: Four principal results about ambiguity in languages (i.e., context free languages) are proved. It is first shown that the problem of determining whether an arbitrary language is inherently ambiguous is recursively unsolvable. Then a decision procedure is presented for determining whether an arbitrary bounded grammar is ambiguous. Next, a necessary and sufficient algebraic condition is given for a bounded language to be inherently ambiguous. Finally, it is shown that no language contained in w1*w2*, each w1 a word, is inherently ambiguous.
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TL;DR: A critical review of recent efforts to automate the writing of translators of programming languages is presented and various approaches to automating the postsyntactic aspects of translator writing are discussed.
Abstract: A critical review of recent efforts to automate the writing of translators of programming languages is presented. The formal study of syntax and its application to translator writing are discussed in Section II. Various approaches to automating the postsyntactic (semantic) aspects of translator writing are discussed in Section III, and several related topics in Section IV.
183 citations
TL;DR: A slightly stronger result is presented which can be used to prove the inherent ambiguity of certain context-free languages and is based on Bar-Hillel, Perles and Shamir's theorem.
Abstract: A useful theorem [ 1, Theo rem 4.1] o f Bar-Hillel, Perles and Shamir gives a necessary condit ion for a set of words on an alphabet 2 to be a context-free language. We present here a slightly stronger result which can also be used to prove the inherent ambiguity o f certain context-free languages. We assume familiarity with the concepts of context-free languages (hereafter simply called languages), generat ion trees, and inherent ambiguity. See [4, pp. 62-65] for a summary of terminology and notation.
167 citations
TL;DR: Jan Tijmen Udding's research interests are mathematical aspects of VLSI, concurrency, program derivation and correctness, and functional programming.
Abstract: Jan Tijmen Udding received the B.S. and M.S. degrees in mathematics, and the Ph.D. degree in computer science from the Eindhoven University of Technology, Eindhoven, The Netherlands, in 1975, 1980, and 1984, respectively. Currently he is an Assistant Professor with the Department of Computer Science at Washington University, St. Louis, Missouri, and an Associate Professor with the Department of Computer Science at the Eindhoven University of Technology. His research interests are mathematical aspects of VLSI, concurrency, program derivation and correctness, and functional programming.
138 citations
TL;DR: A mathematical model is presented which embodies salient features of many modern compiling techniques, including deterministic linear bounded automaton and nondeterministic stack automaton, and particular instances of this more general device are noted.
Abstract: Compilation consists of two parts, recognition and translation. A mathematical model is presented which embodies salient features of many modern compiling techniques. The model, called the stack automaton, has the desirable feature of being deterministic in nature. This deterministic device is generalized to a nondeterministic device (nondeterministic stack automaton) and particular instances of this more general device are noted. Sets accepted by nondeterministic stack automata are recursive. Each set accepted by a deterministic linear bounded automaton is accepted by some nonerasing stack automaton. Each context-sensitive language is accepted by some (deterministic) stack automaton.
134 citations
22 Aug 1995
TL;DR: The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place and the reachability problem for this class is proved to be NP-complete.
Abstract: The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NP-complete. Further consequences are: the uniform word problem for commutative context-free grammars is NP-complete; weak-bisimilarity is semidecidable for Basic Parallel Processes.
127 citations
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TL;DR: It is found that no finite-state Markov process that produces symbols with transition from state to state can serve as an English grammar, and the particular subclass of such processes that produce n -order statistical approximations to English do not come closer, with increasing n, to matching the output of anEnglish grammar.
Abstract: We investigate several conceptions of linguistic structure to determine whether or not they can provide simple and "revealing" grammars that generate all of the sentences of English and only these. We find that no finite-state Markov process that produces symbols with transition from state to state can serve as an English grammar. Furthermore, the particular subclass of such processes that produce n -order statistical approximations to English do not come closer, with increasing n , to matching the output of an English grammar. We formalize-the notions of "phrase structure" and show that this gives us a method for describing language which is essentially more powerful, though still representable as a rather elementary type of finite-state process. Nevertheless, it is successful only when limited to a small subset of simple sentences. We study the formal properties of a set of grammatical transformations that carry sentences with phrase structure into new sentences with derived phrase structure, showing that transformational grammars are processes of the same elementary type as phrase-structure grammars; that the grammar of English is materially simplified if phrase structure description is limited to a kernel of simple sentences from which all other sentences are constructed by repeated transformations; and that this view of linguistic structure gives a certain insight into the use and understanding of language.
2,140 citations
TL;DR: Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.
Abstract: Finite automata are considered in this paper as instruments for classifying finite tapes. Each one-tape automaton defines a set of tapes, a two-tape automaton defines a set of pairs of tapes, et cetera. The structure of the defined sets is studied. Various generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined. Some decision problems concerning automata are shown to be solvable by effective algorithms; others turn out to be unsolvable by algorithms.
1,930 citations
TL;DR: A sequence of restrictions that limit grammars first to Turing machines, then to two types of system from which a phrase structure description of the generated language can be drawn, and finally to finite state Markov sources are shown to be increasingly heavy.
Abstract: A grammar can be regarded as a device that enumerates the sentences of a language. We study a sequence of restrictions that limit grammars first to Turing machines, then to two types of system from which a phrase structure description of the generated language can be drawn, and finally to finite state Markov sources (finite automata). These restrictions are shown to be increasingly heavy in the sense that the languages that can be generated by grammars meeting a given restriction constitute a proper subset of those that can be generated by grammars meeting the preceding restriction. Various formulations of phrase structure description are considered, and the source of their excess generative power over finite state sources is investigated in greater detail.
1,330 citations
TL;DR: This chapter discusses the several classes of sentence-generating devices that are closely related, in various ways, to the grammars of both natural languages and artificial languages of various kinds.
Abstract: Publisher Summary This chapter discusses the several classes of sentence-generating devices that are closely related, in various ways, to the grammars of both natural languages and artificial languages of various kinds. By a language it simply mean a set of strings in some finite set V of symbols called the vocabulary of the language. By a grammar a set of rules that give a recursive enumeration of the strings belonging to the language. It can be said that the grammar generates these strings. The chapter discusses the aspect of the structural description of a sentence, namely, its subdivision into phrases belonging to various categories. A major concern of the general theory of natural languages is to define the class of possible strings; the class of possible grammars; the class of possible structural descriptions; a procedure for assigning structural descriptions to sentences, given a grammar; and to do all of this in such a way that the structural description assigned to a sentence by the grammar of a natural language will provide the basis for explaining how a speaker of this language would understand this sentence.
819 citations
TL;DR: In this article, the correspondence decision problem is defined as the problem of determining for an arbitrary finite set (gu g{), (g2, g2), • • •, (gM, gi) of pairs of corresponding non-null strings on a, b whether there is a solution in w, iu ii, • •• •, in of equation
Abstract: By a string on a, 6 we mean a row of a's and 6's such as baabbbab. I t may involve only a, or 6, or be null. If, for example, gi, g2, gz represent strings baby aa, b respectively, string g2gigigzg2 on gi, g2, gz will represent, in obvious fashion, the string aababbabbaa on a, 6. By the correspondence decision problem we mean the problem of determining for an arbitrary finite set (gu g{), (g2, g2), • • • , (gM, gi) of pairs of corresponding non-null strings on a, b whether there is a solution in w, iu ii, • • • , in of equation
602 citations