zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Boolean functions and computation models. (English) Zbl 1016.94046
Texts in Theoretical Computer Science. An EATCS Series. Berlin: Springer-Verlag. xiv, 601 p. EUR 41.95 (net); sFr 72.00; £ 29.50; $ 44.95 (2002).
The authors give a survey of the present research concerning the study of Boolean functions, formulas, circuits and propositional proof systems. The first three chapters are dedicated to Boolean functions and circuit lower and upper bounds. Chapter 4 deals with the threshold phenomenon for 3-SAT (conjunctive normal forms on $n$ variables and 3 literals per clause). In Chapter 5 several propositional proof systems are studied which have relevance to complexity theory: Gentzen calculus, resolution, algebraic refutation systems, Frege systems. Various computational models (uniform circuit families, Turing machines, parallel random access machines) are given in Chapter 6 and some features of parallel computation are illustrated by giving example programs. The last chapter includes an interesting study of the higher type functional complexity theory. Several open problems are presented.

94C10Switching theory, application of Boolean algebra; Boolean functions
68Q10Modes of computation
68Q17Computational difficulty of problems
94C05Analytic circuit theory
03D15Complexity of computation