Walter J. Savitch

Time Bounded Random Access Machines with Parallel Processing

The RAM model of Cook and Reckhow ~s extended to allow parallel recursive calls and the elementary theory of such machines is developed The uniform cost criterion is used The results include proofs of (!) the eqmvalence of nondetermmtsUc and determm~sttc polynomml Ume for such parallel machines and (2) the eqmvalence of polynomml tmae on such parallel machines and polynomml space on ordinary nonparallel RAMs Also included are results showing that parallelism appears to be stnctly more powerful than nondeter-

The Formal complexity of natural language

Prologue.- What is Mathematical Linguistics?.- I. Early Nontransformational Grammar.- to Part I.- Formal Linguistics and Formal Logic.- An Elementary Proof of the Peters-Ritchie Theorem.- On Constraining the Class of Transformational Languages.- Generative Grammars without Transformation Rules-A Defense of Phrase Structure.- A Program for Syntax.- II Modern Context-Free-Like Models.- to Part II.- Natural Languages and Context-Free Languages.- Unbounded Dependency and Coordinate Structure.- On Some Formal Properties of MetaRules.- Some Generalizations of Categorial Grammars.- III More than Context-Free and Less than Transformational Grammar.- to Part III.- Cross-serial Dependencies in Dutch.- Evidence Against the Context-Freeness of Natural Language.- English is not a Context-Free Language.- The Complexity of the Vocabulary of Bambara.- Context-Sensitive Grammar and Natural Language Syntax.- How Non-Context Free is Variable Binding?.- Prologue.- Computationally Relevant Properties of Natural Languages and Their Grammars.- Index of Languages.- Name Index.

Growth functions of stochastic Lindenmayer systems

A stochastic version of the 0L systems of Lindenmayer is introduced and the growth functions of such systems are studied. Topics covered include techniques for computing such growth functions, classification of such stochastic 0L systems according to growth rate, and decidability results about various notions of growth equivalence.

A note on multihead automata and context-sensitive languages

SummaryIn this note we show that the following two statements are equivalent: (1) Any language over a one-letter alphabet, which is accepted by some nondeterministic multihead automaton can also be accepted by some deterministic multihead automaton. (2) Deterministic and nondeterministic context-sensitive languages are the same.

Why it might pay to assume that languages are infinite

We show that, in a wide variety of situations, formal languages which are finite can be given smaller descriptions if we assume that they are but the observed data for an infinite language. This points to one possible reason for assuming that natural language is infinite.

Some characterizations of lindenmayer systems in terms of chomsky-type grammars and stack machines

Characterizations of Lindenmayer systems in terms of Chomsky-type grammars and stack machines are presented. Systems with cellular interaction as well as without cellular interaction are studied.

An occurrence-based model of word categorization

Small corpora present problems for traditional statistical analysis because of their sparsity of data. We discuss a methodology for classifying words in edited, plain text corpora which has the potential for working on relatively small corpora. This approach, which we calloccurrence-based processing, counts which contexts occur around a given word, but pays no attention to the number of times that each context occurs. We obtain good results on an artificial language and compare our results to Elmans connectionist analysis of the same artificial language. We obtain more modest results on real world corpora, but the results are sufficient to draw some methodological and language theoretical conclusions.

A note on relativized log space

AbstractIt is shown that there is a recursive oracleD such that, thereby answering an open question of Ladner and Lynch [5]. Here

Parallel and nondeterministic time complexity classes

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