Some remarks on state grammars and matrix grammars

Moriya, Etsuro

doi:10.1016/s0019-9958(73)90884-x

Cited by 10 publications

(8 citation statements)

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“…An early proposal was that of 'matrix grammars' [10] whose rules are grouped in sequences (called 'matrices') and derivation steps iterate through the rules in a sequence. Many other mechanisms have been proposed, amongst which are: indexed grammars [1], programmed grammars [16], regulated grammars [7], grammars with state [11,14], grammars with control sets [9] and co-operating grammars [13]. Some of these approaches treat the derivation sequences themselves as strings in an additional language (e.g.…”

Section: Some Historical Commentsmentioning

confidence: 99%

“…These are a special case of programmed grammars [16] where only 'success sets' are associated with production rules. The -free switching grammars are, effectively, an alternative presentation of ( -free) state grammars [11,14]. This simple form of reactivity is considered here to illustrate some of the issues which arise in reactive grammars and because it is related to the next form of reactivity that we consider, that of 'string transformer grammars'.…”

Section: Switching Grammarsmentioning

confidence: 99%

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Reactivity and Grammars: An Exploration

Barringer

Rydeheard

Gabbay

2014

Lecture Notes in Computer Science

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We consider the relationship between grammars and formal languages, exploring the following idea: Normally, when considering the process of deriving a string using a grammar, all structures remain fixed except for the string which is changed only by replacement of substrings. By introducing a more dynamic view of this process, we may allow the grammar to change in various ways as the derivation proceeds, or we may change the notion of application of a rule to a string, or the intermediate strings may be modified between application of rules. We call these more dynamic approaches to language generation 'reactive grammars' and explore, in this paper a range of such reactivities. Some of these are related to previously introduced notions of generative grammars, others appear to be new. Reactivity of computational structures has been explored in other areas, e.g. in Kripke structures and in the general areas of evolvable and adaptive systems. Background and motivationA standard approach to defining models of computation is to introduce fixed structures over which computation may take place. Such structures include graphs, algebras, grammars, automata, etc. An alternative is to allow the structures themselves to change as computation proceeds. Such computational systems are called 'evolutionary', 'adaptive' or (the term we shall use) 'reactive'. The advantages of this additional flexibility are several: (1) they allow us to model desirable aspects of computation in dynamic settings where we require systems which may reconfigure themselves during computation, (2) they allow us to model the influence of external activity under which computation may have to adapt by changing computational structure, (3) they allow us to re-examine the relationship of a computational model with its semantics. The semantics may be a function computed, or a language generated or recognised, or a logical expression satisfied (e.g. for modal logics and Kripke models). The extra degree of freedom that reactivity introduces allows us additional mechanisms for generating a required semantics. It is this feature of reactive systems that we consider in this paper, where we explore ideas of reactivity in grammars and the relationship of these with the generation of formal languages.For grammars, reactivity is realised through transformations that interact with the derivation steps by which a grammar generates a word in a language. The interaction may for example, at each step of a derivation, control which grammar rules may be applied, or change the notion of application of a rule to a string, or modify rules as they are used, or transform the intermediate strings as they are generated in a derivation. Introducing such reactive elements into the definitions of grammars allows us to re-examine the mathematical structures involved in language recognition and generation, to relate languages according to their reactive structure as well as their production rules, and to model more dynamically changing computational systems.Before exploring rea...

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Section: Some Historical Commentsmentioning

confidence: 99%

Section: Switching Grammarsmentioning

confidence: 99%

Reactivity and Grammars: An Exploration

Barringer

Rydeheard

Gabbay

2014

Lecture Notes in Computer Science

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“…The mechanisms for controlling derivations vary from author to author. Many other mechanisms have been proposed, amongst which are: indexed grammars [5], programmed grammars [142], regulated grammars [47], grammars with state [118,129], grammars with control sets [98] and co-operating grammars [128]. Many other mechanisms have been proposed, amongst which are: indexed grammars [5], programmed grammars [142], regulated grammars [47], grammars with state [118,129], grammars with control sets [98] and co-operating grammars [128].…”

Section: Some Historical Commentsmentioning

confidence: 99%

Reactive Kripke Semantics

Gabbay

2013

Cognitive Technologies

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“…It has been shown in [199], for example, that the removal of the leftmost restriction in Kasai state grammars produces grammars equivalent to matrix grammars. analyzed matrix grammars in which certain substitutions can be endowed with a condition of the type EL.…”

Section: (~ + ~Z)c~ (So) and ~ (~ + ~:~)C~ ( Sc)mentioning

confidence: 99%

Classes of formal grammars

Maslov¹,

Stotskii²

1976

J Math Sci

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Generating grammars, recognition automata, and other facilities for the specification of languages are reviewed.The present survey covers research published on mathematical linguistics, for the most part from 1971 through 1973. Primary attention is given to work on the theory of formal grammars and accepting automata. As in the earlier survey [16], we disregard articles pertaining wholly to linguistic applications of grammar theory.As a rule, with the exception of three or four articles, references cited in [16] are not repeated in the present Literature Cited. Accordingly, when referring to the results of a particular author for whom no reference is given, it is understood that the appropriate source is often to be found in [16].Among the more recent books published on mathematical linguistics we cite first and foremost the monograph by Gladkii [14], which contains a penetrating discussion of the theory of formal grammars and affords the reader a well-rounded comprehension of the scope of this discipline. A high level of presentation of the theory of languages and automata is found in a book by Kain [170], which is designed primarily as a lecture course for the training of computer design specialists and progr am me r s.Our survey is divided into sections corresponding to definite areas of research. Space limitations prevent us from cross-referencing from one section to another and necessitates the presentation of certain concepts without formal definitions (this is particularly true in the case of standard terms or concepts described in the earlier survey [16]). w Fundamental ConceptsA grammar is understood to be an ordered quadruple F = (V, W, S, R), where V is a terminal alphabet, W is a nonterminal (auxiliary) alphabet, V A W = | S is an initial symbol, S~W, and R is a system of derivation rules. A particular type T is assigned to a grammar according to tlie form of the rules. A finite-automaton grammar is assigned type 3, a contextless* grammar type 2, and a context (context-* We use the term "contextless" to designate what are called e-free context-free (CF) grammars in the non-Soviet literature.

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Some remarks on state grammars and matrix grammars

Cited by 10 publications

References 9 publications

Reactivity and Grammars: An Exploration

Reactivity and Grammars: An Exploration

Reactive Kripke Semantics

Classes of formal grammars

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