Grammars with Context Conditions and Their Applications

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According to the types of context conditions, this self-contained reference classifies them into grammars with context conditions placed on the domains of grammatical derivations, the use of grammatical productions, and the neighborhood of the rewritten symbols. The focus is on grammatical generative power, important properties, simplification, reduction, implementation, and applications, most of which are related to microbiology. He has taught theoretical computer science at various European and American universities, including the University of Missouri, where he spent a decade teaching advanced topics of formal language theory.

He is the author of Automata and Languages and over sixty papers related to the subject of this book.

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Permissions Request permission to reuse content from this site. Table of contents Preface. Conditions Placed on Derivation Domains. Conditional grammars are the simplest version of grammars controlled by context conditions. The structure of a conditional grammar is very similar to that of a normal rewrite grammar: When R is regular, R can just be expressed as a regular expression.

Informally then, the production rule for some pair in P can apply only to strings that are in its context language.

It cannot apply to strings like xSy , aaaSxbbb , etc. A semi-conditional grammar is very similar to a conditional grammar, and technically the class of semi-conditional grammars are a subset of the conditional grammars. Rather than specifying what the whole of the string must look like for a rule to apply, semi-conditional grammars specify that a string must have as substrings all of some set of strings, and none of another set, in order for a rule to apply.

The derives relation can then be defined as follows. An example of a semi-conditional grammar is given below also as an example of random context grammars. A random context grammar is a semi-conditional grammar in which the R and Q sets are all subsets of N. One grammar which can do this is:.

The behavior of the R sets here is trivial: The behavior of the Q sets, however, are more interesting. We can cycle through these stages as many times as we want, rewriting all S s to XX s before then rewriting each X to a Y, and then each Y to an S , finally ending by replacing each S with an A and then an a.

Because the rule for replacing S with A prohibits application to a string with an X in it, we cannot apply this in the middle of the first stage of the S -doubling process, thus again preventing us from only doubling some S s.

Ordered grammars are perhaps one of the simpler extensions of grammars into the controlled grammar domain. The partial ordering is then used to determine which rule to apply to a string, when multiple rules are applicable. The derives relation is then:. Like many other contextually controlled grammars, ordered grammars can enforce the application of rules in a particular order.

And as it turns out, just such an ordered grammar exists:. At each step of the way, the derivation proceeds by rewriting in cycles.

Notice that if at the fifth step SY , we had four options: The same hold for other combinations, so that overall, the ordering forces the derivation to halt, or else proceed by rewriting all S s to XX s, then all X s to Y s, then all Y s to S s, and so on, then finally all S s to A s then all A s to a s. A still further class of controlled grammars is the class of grammars with parallelism in the application of a rewrite operation, in which each rewrite step can or must rewrite more than one non-terminal simultaneously.

These, too, come in several flavors: Indian parallel grammars, k-grammars, scattered context grammars, unordered scattered context grammars, and k-simple matrix grammars.

Grammars with Context Conditions and Their Applications

Again, the variants differ in how the parallelism is defined. An Indian parallel grammar is simply a CFG in which to use a rewrite rule, all instances of the rules non-terminal symbol must be rewritten simultaneously. A k-grammar is yet another kind of parallel grammar, very different from an Indian parallel grammar, but still with a level of parallelism. The text maintains a balance between fundamental concepts, theoretical results, and applications of these grammars.

From a theoretical viewpoint, it introduces several variants of scattered context grammatical models.

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Based on these models, it demonstrates the concepts, methods, and techniques employed in handling scattered pieces of information with enough rigor to make them quite clear. It also explains a close relationship between the subject of the book and several important mathematical fi elds, such as algebra and graph theory.

A property of random context picture grammars - ScienceDirect

From a more practical point of view, the book describes scattered information processing by fundamental information technologies. Throughout the book, several in-depth case studies and examples are carefully presented. Whilst discussing various methods concerning grammatical processing of scattered information, the text illustrates their applications with a focus on applications in linguistics. The book is relevant to specialists and advanced students in theoretical computer science, mathematics, and linguistics.

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Title and Contents pages Click here to view A. His research has focused on mathematically oriented computer science, especially automata, formal languages, compilers, computer algebra, graphs, and metamathematics.

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