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A non-strict form allows one exception to this format restriction for allowing the empty word (epsilon, ε) to be a member of the described language. The normal form was established by Sheila Greibach and it bears her name. More precisely, a context-free grammar is in Greibach normal form, if all production rules are of the form:
Sheila Adele Greibach (born 6 October 1939 in New York City) is an American researcher in formal languages in computing, automata, compiler theory and computer science.She is an Emeritus Professor of Computer Science at the University of California, Los Angeles, and notable work include working with Seymour Ginsburg and Michael A. Harrison in context-sensitive parsing using the stack automaton ...
In fact, there exists a normal form for this decomposition, [2] which is commonly known as Nivat's Theorem: [3] ... Ginsburg, Seymour; Greibach, Sheila (1967 ...
The grammar is in Greibach normal form if every production rule is of the form ::= … A N − 1 {\displaystyle A::=sA_{0}\ldots A_{N-1}} , where capital letters are variables, s ∈ Σ {\displaystyle s\in \Sigma } , and N ≥ 0 {\displaystyle N\geq 0} , that is, the right side of the production is a single terminal symbol followed by zero or ...
In theoretical computer science, in particular in formal language theory, Greibach's theorem states that certain properties of formal language classes are undecidable. It is named after the computer scientist Sheila Greibach , who first proved it in 1963.
Sheila Greibach, grammar theory, Greibach normal form; David Gries, first text on writing compilers, [10] [11] contributions to semantics of programming language constructs, e.g. Interference freedom and [12] Robert Griesemer, co-designer of Go; Ralph Griswold, designer of SNOBOL, SL5, and Icon
Sheila Greibach – Greibach normal form, Abstract family of languages (AFL) theory; David Gries – The Science of Programming, Interference freedom, Member Emeritus, IFIP WG 2.3 on Programming Methodology; Robert Griesemer – Go language; Ralph Griswold – SNOBOL
Every context-free grammar with no ε-production has an equivalent grammar in Chomsky normal form, and a grammar in Greibach normal form. "Equivalent" here means that the two grammars generate the same language. The especially simple form of production rules in Chomsky normal form grammars has both theoretical and practical implications.