Greibach, Sheila 1939
Overview
Works:  25 works in 68 publications in 3 languages and 704 library holdings 

Roles:  Author 
Classifications:  QA76.6, 001.642 
Publication Timeline
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Most widely held works by
Sheila Greibach
Theory of program structures : schemes, semantics, verification by
Sheila Greibach(
Book
)
24 editions published between 1974 and 2007 in 3 languages and held by 366 WorldCat member libraries worldwide
24 editions published between 1974 and 2007 in 3 languages and held by 366 WorldCat member libraries worldwide
Studies in abstract families of languages by
Seymour Ginsburg(
Book
)
13 editions published in 1969 in English and held by 203 WorldCat member libraries worldwide
13 editions published in 1969 in English and held by 203 WorldCat member libraries worldwide
Inverses of phrase structure generators by
Sheila Greibach(
Book
)
7 editions published between 1963 and 1968 in English and Undetermined and held by 14 WorldCat member libraries worldwide
7 editions published between 1963 and 1968 in English and Undetermined and held by 14 WorldCat member libraries worldwide
Abstract families of languages by
Seymour Ginsburg(
Book
)
3 editions published between 1967 and 1968 in English and held by 4 WorldCat member libraries worldwide
The notion of an abstract family of languages (AFL) as a family of sets of words satisfying certain properties common to many types of formal languages is introduced. Operations preserving AFL are then considered. The concept of an abstract family of acceptors (AFA) is also introduced and shown to give rise to an AFL. A necessary and sufficient condition on an AFL is presented in order that the AFL come from some AFA. Finally, abstract families of transducers (AFA with output) are discussed. (Author)
3 editions published between 1967 and 1968 in English and held by 4 WorldCat member libraries worldwide
The notion of an abstract family of languages (AFL) as a family of sets of words satisfying certain properties common to many types of formal languages is introduced. Operations preserving AFL are then considered. The concept of an abstract family of acceptors (AFA) is also introduced and shown to give rise to an AFL. A necessary and sufficient condition on an AFL is presented in order that the AFL come from some AFA. Finally, abstract families of transducers (AFA with output) are discussed. (Author)
Principal AFL by
Seymour Ginsburg(
Book
)
1 edition published in 1969 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1969 in English and held by 4 WorldCat member libraries worldwide
Full afls and nested iterated substitution(
Book
)
1 edition published in 1969 in English and held by 2 WorldCat member libraries worldwide
Recently there have been several investigations of the closure under substitution of various families of languages, and of the relation of substitution to AFLs in general. A machine realization of the substitution closure of a full AFL l was obtained by finitely nesting tapes of any machine representation for l. It was shown that if any full AFL l is not closed under substitution, the result of substituting members of l into l, is not substitution closed and hence l generates an infinite hierarchy of full AFLs and the substitution closure of l is not full principal. In the paper we define a generalization of the substitution operator, called nested interated substitution, examine the properties of families of languages closed under nested iterated substitution, establish the appropriate machine characterization and discuss related decision problems
1 edition published in 1969 in English and held by 2 WorldCat member libraries worldwide
Recently there have been several investigations of the closure under substitution of various families of languages, and of the relation of substitution to AFLs in general. A machine realization of the substitution closure of a full AFL l was obtained by finitely nesting tapes of any machine representation for l. It was shown that if any full AFL l is not closed under substitution, the result of substituting members of l into l, is not substitution closed and hence l generates an infinite hierarchy of full AFLs and the substitution closure of l is not full principal. In the paper we define a generalization of the substitution operator, called nested interated substitution, examine the properties of families of languages closed under nested iterated substitution, establish the appropriate machine characterization and discuss related decision problems
AMBIGUITY IN GRAPHS AND EXPRESSIONS(
Book
)
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
A regular expression is called unambiguous if every tape in the event can be generated from the expression in one way only. The flowgraphtechnique for constructing an expression is shown to preserve ambiguities of the graph, and thus, if the graph is that of a deterministic automaton, the expression is unambiguous. A procedure for generating a nondeterministic automaton which preserves the ambiguities of the given regular expression is described. Finally, a procedure for testing whether a given expression is ambiguous is given. (Author)
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
A regular expression is called unambiguous if every tape in the event can be generated from the expression in one way only. The flowgraphtechnique for constructing an expression is shown to preserve ambiguities of the graph, and thus, if the graph is that of a deterministic automaton, the expression is unambiguous. A procedure for generating a nondeterministic automaton which preserves the ambiguities of the given regular expression is described. Finally, a procedure for testing whether a given expression is ambiguous is given. (Author)
Mappings which preserve context sensitive languages(
Book
)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
A basic result which gives a condition under which a (possibly lengthdecreasing) homomorphism preserves a context sensitive language is presented. Using this result, conditions under which pushdown transducers and linear bounded transducers preserve context sensitive languages are given. The basic result is also applied to show that certain rewriting systems generate context sensitive languages instead of arbitrary recursively enumerable sets. Of special interest is the result that if each rule in a rewriting system has a terminal letter of its right side, then the language generated is context free. (Author)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
A basic result which gives a condition under which a (possibly lengthdecreasing) homomorphism preserves a context sensitive language is presented. Using this result, conditions under which pushdown transducers and linear bounded transducers preserve context sensitive languages are given. The basic result is also applied to show that certain rewriting systems generate context sensitive languages instead of arbitrary recursively enumerable sets. Of special interest is the result that if each rule in a rewriting system has a terminal letter of its right side, then the language generated is context free. (Author)
A note on pushdown store automata and regular systems(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
A theorem of BarHillel, Perles, and Shamir is used to show that the set of tapes left on the pushdown store by a regular set is regular. As a consequence, one obtains a generalization of a theorem of Buchi. (Author)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
A theorem of BarHillel, Perles, and Shamir is used to show that the set of tapes left on the pushdown store by a regular set is regular. As a consequence, one obtains a generalization of a theorem of Buchi. (Author)
Checking automata and oneway stack languages(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
A checking automaton is equivalent to a oneway nonerasing stack automaton which, once it enters its stack, never again writes on its stack. The checking automaton languages (cal) form a full AFL (Abstract Family of Languages) closed under substitution. If L is contained in a* is an infinite cal, then L contains an infinite regular set. Consequently, there are oneway nonerasing stack languages which are not cal. (Author)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
A checking automaton is equivalent to a oneway nonerasing stack automaton which, once it enters its stack, never again writes on its stack. The checking automaton languages (cal) form a full AFL (Abstract Family of Languages) closed under substitution. If L is contained in a* is an infinite cal, then L contains an infinite regular set. Consequently, there are oneway nonerasing stack languages which are not cal. (Author)
A note on undecidable properties of formal languages(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
A general set of conditions is given under which a property is undecidable for a family of languages. Examples are given of the application of this result to wellknown families of languages. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
A general set of conditions is given under which a property is undecidable for a family of languages. Examples are given of the application of this result to wellknown families of languages. (Author)
STACK AUTOMATA AND COMPILING(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
Compilation consists of two parts, recognition and translation. A mathematical model is presented which embodies the 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 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. (Author)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
Compilation consists of two parts, recognition and translation. A mathematical model is presented which embodies the 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 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. (Author)
INDEPENDENCE OF AFL OPERATION(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The axiomatic properties used to define abstract families of languages are considered. The properties are shown not to be independent. All independent subsets that imply the remaining properties are found. Finally alternative operations are considered. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The axiomatic properties used to define abstract families of languages are considered. The properties are shown not to be independent. All independent subsets that imply the remaining properties are found. Finally alternative operations are considered. (Author)
ONEWAY STACK AUTOMATA(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
A number of operations which either preserve sets accepted by oneway stack automata or preserve sets accepted by deterministic oneway stack automata are presented. For example, sequential transduction preserves the former; set complementation, the latter. Several solvability questions are also considered. (Author)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
A number of operations which either preserve sets accepted by oneway stack automata or preserve sets accepted by deterministic oneway stack automata are presented. For example, sequential transduction preserves the former; set complementation, the latter. Several solvability questions are also considered. (Author)
SCATTERED CONTEXT GRAMMARS(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
Scattered context grammars are defined and the closure properties of the family of languages generated are considered. This family of languages is contained in the family of contextsensitive languages and contains all languages accepted by linear time nondeterministic Turing machines. (Author)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
Scattered context grammars are defined and the closure properties of the family of languages generated are considered. This family of languages is contained in the family of contextsensitive languages and contains all languages accepted by linear time nondeterministic Turing machines. (Author)
CHAINS OF FULL AFLS(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
If a full Abstract Family of Languages (AFL) L is not closed under substitution, then the result of substituting members of L into L, is not substitution closed and hence L generates an infinite hierarchy of full AFLs. If L1 and L2 are two incomparable full AFLs, then the least full AFL containing L1 and L2 is not substitution closed. In particular, the substitution closure of any full AFL properly contained in the contextfree languages is itself properly contained in the contextfree languages. If any set of languages generates the contextfree languages, one of its members must do so. The substitution closure of the oneway stack languages is properly contained in the nested stack languages. For each n, there is a class of full contextfree AFLs whose partial ordering under inclusion is isomorphic to the natural partial ordering on ntuples of positive integers. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
If a full Abstract Family of Languages (AFL) L is not closed under substitution, then the result of substituting members of L into L, is not substitution closed and hence L generates an infinite hierarchy of full AFLs. If L1 and L2 are two incomparable full AFLs, then the least full AFL containing L1 and L2 is not substitution closed. In particular, the substitution closure of any full AFL properly contained in the contextfree languages is itself properly contained in the contextfree languages. If any set of languages generates the contextfree languages, one of its members must do so. The substitution closure of the oneway stack languages is properly contained in the nested stack languages. For each n, there is a class of full contextfree AFLs whose partial ordering under inclusion is isomorphic to the natural partial ordering on ntuples of positive integers. (Author)
PREAFL (ABSTRACT FAMILY OF LANGUAGES)(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
A preAFL is a family of sets of words closed under certain basic operations. Each preAFL contains all regular sets and becomes an abstract family of languages when closed under lengthincreasing homomorphism. A number of situations in automata and language theory giving rise to preAFL are presented. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
A preAFL is a family of sets of words closed under certain basic operations. Each preAFL contains all regular sets and becomes an abstract family of languages when closed under lengthincreasing homomorphism. A number of situations in automata and language theory giving rise to preAFL are presented. (Author)
DETERMINISTIC CONTEXT FREE LANGUAGES(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
A number of results about deterministic languages (languages accepted by pushdown automata with no choice of moves) are established. In particular, (1) each deterministic language is unambiguous. (2) the complement of each deterministic language is a deterministic language. (3) numerous operations which preserve deterministic languages (for example, intersection with a regular set) are obtained. (4) several problems are shown to be recursively unsolvable. (Author)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
A number of results about deterministic languages (languages accepted by pushdown automata with no choice of moves) are established. In particular, (1) each deterministic language is unambiguous. (2) the complement of each deterministic language is a deterministic language. (3) numerous operations which preserve deterministic languages (for example, intersection with a regular set) are obtained. (4) several problems are shown to be recursively unsolvable. (Author)
MULTITAPE AFA(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
In previous papers the notion of a family of oneway nondeterministic devices was abstracted and studied extensively. A natural extension of a device with a particular type of storage tape is a multitape (storage) device, each tape of the same kind. In most familiar casescounter, pushdown, stackadding a second storage tape increases the power of the device to that of a Turing acceptor. By suitable restrictions on multitape devices, families can be obtained so that the associated languages do not include all recursively enumerable sets. The purpose of the paper is to abstract the notion of an 'abstract family of multitape acceptors' (abbreviated 'multitape AFA'), each storage tape not necessarily of the same kind, and examine the family of associated languages
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
In previous papers the notion of a family of oneway nondeterministic devices was abstracted and studied extensively. A natural extension of a device with a particular type of storage tape is a multitape (storage) device, each tape of the same kind. In most familiar casescounter, pushdown, stackadding a second storage tape increases the power of the device to that of a Turing acceptor. By suitable restrictions on multitape devices, families can be obtained so that the associated languages do not include all recursively enumerable sets. The purpose of the paper is to abstract the notion of an 'abstract family of multitape acceptors' (abbreviated 'multitape AFA'), each storage tape not necessarily of the same kind, and examine the family of associated languages
PRINCIPAL AFL(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
A (full) principal AFL is a (full) AFL generated by a single language, i.e., it is the smallest (full) AFL containing the given language. In the present paper, a study is made of such AFL. First, an AFA (abstract family of acceptors) characterization of (full) principal AFL is given. From this result, many wellknown families of AFL can be shown to be (full) principal AFL. Next, a representation theorem for each language in a (full) principal AFL is given involving the generator and one application each of concatenation, star, intersection with a regular set, inverse homomorphism, and a special type of homomorphism. Finally, it is shown that if l1 and l2 are (full) principal AFL, then so are (a) the smallest (full) AFL containing ((the intersection of L1 and L2)/L1 in l1, 12 in 12) and (b) the family obtained by substituting epsilonfree languages of 12 into languages of l1. (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
A (full) principal AFL is a (full) AFL generated by a single language, i.e., it is the smallest (full) AFL containing the given language. In the present paper, a study is made of such AFL. First, an AFA (abstract family of acceptors) characterization of (full) principal AFL is given. From this result, many wellknown families of AFL can be shown to be (full) principal AFL. Next, a representation theorem for each language in a (full) principal AFL is given involving the generator and one application each of concatenation, star, intersection with a regular set, inverse homomorphism, and a special type of homomorphism. Finally, it is shown that if l1 and l2 are (full) principal AFL, then so are (a) the smallest (full) AFL containing ((the intersection of L1 and L2)/L1 in l1, 12 in 12) and (b) the family obtained by substituting epsilonfree languages of 12 into languages of l1. (Author)
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Related Identities
 Ginsburg, Seymour 1927 Author
 Hopcroft, John E. 1939
 SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF
 HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
 Air Force Cambridge Research Laboratories (U.S.)
 United States Air Force Office of Scientific Research
 Harrison, Michael A.
 Even, Shimon
 Ott, Gene
 Book, Ronald
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Canada Computational linguistics Computer programming Computer programs Computer science Formal languages Generative grammar Language and languages Linguistic analysis (Linguistics) Logic design Machine theory Machine translating Mathematical linguistics Recursive programming Robots Scientists Sequential machine theory Software engineering United States
Alternative Names
Greibach, S. A.
Greibach, Sheila.
Greibach, Sheila A. 1939
Greibach, Sheila Adele 1939
Sheila A. Greibach USamerikanische Informatikerin und Mathematikerin
Sheila Greibach amerikansk informatikar
Sheila Greibach amerikansk informatiker
Sheila Greibach especialista en informtica estadounidense
Sheila Greibach informatica statunitense
Sheila Greibach informaticienne amricaine
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