D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, London, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....as powerful as polynomial time Turing machines. Due to lack of space, most proofs in this abstract have to remain sketchy or are even omitted. 2 Preliminaries We assume the reader is familiar with basic automata and machine models from formal language theory and complexity theory, see, e.g. [11, 1, 3]. Our Turing machines are standard multi tape machines, see [11] For the definition of sublinear time classes we use indexing machines. These machines cannot directly access their input tape, but instead have to write down a number in binary on a so called index tape. When they enter a specified ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, London, 1994.

....our general relationship between circuit and polynomial time classes. In Sect. 4 we consider the power of precomputation. We end with a short conclusion. 2 Preliminaries and Some Basic Facts We assume the reader is familiar with basic complexity theory notions, see e.g. the textbooks [BDG95, BC94, Pap94] As a computation model for parallel computation, very often families of boolean circuits are used. One single boolean circuit has of course a fixed number of input bits, say n, thus it can only work on input words of length exactly n. To define acceptance of languages via circuits, we ....

.... From the polynomial time context, we will need the following classes: The polynomial time hierarchy is the hierarchy of classes one obtains starting with P (deterministic polynomial time) and applying to this class the polynomially bounded quantifiers 9 p and 8 p , see [Wra77] or the textbook [BC94] PH is the union of all classes in the polynomial time hierarchy. The counting hierarchy is the class obtained in the same way but now allowing additionally the polynomially bounded counting quantifier C p , essentially a majority quantifier over an exponential range [Wag86, Tor91] CH is the ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, 1994.

....as powerful as polynomial time Turing machines. Due to lack of space, most proofs in this abstract have to remain sketchy or are even omitted. 2 Preliminaries We assume the reader is familiar with basic automata and machine models from formal language theory and complexity theory, see, e.g. [11, 1, 3]. Our Turing machines are standard multi tape machines, see [11] For the definition of sublinear time classes we use indexing machines. These machines cannot directly access their input tape, but instead have to write down a number in binary on a so called index tape. When they enter a specified ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, London, 1994.

....world. In the same spirit we finally turn to the question of oracle separability of PSPACE from MidbitP and PP PhiP and give equivalent statements in terms of circuits. 2 Preliminaries We assume the reader is familiar with basic complexity theory notions; refer to the standard literature [BC94, Pap94, BDG95] In the early nineties a general method to obtain oracle separations was given independently in [BCS92, Ver93] This became later known as the leaf language approach to the definition of complexity classes [HLS 93, Pap94] In the sequel we use it as our main technical tool. For ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, London, 1994.

....s = def Phi x = x 1 ; x k ) fi fi x 2 Omega max 1jk x j s(k) Psi . For x = x 1 ; x k ) the dimension of x is defined as dim x = def k. We assume the reader to be familiar with basic complexity classes and reducibilities. Refer to the standard literature, e.g. BC94, Pap94, BDG95] Let FP be the class of total functions computed in polynomial time by deterministic Turing transducers. With FP ff we denote the class of functions computed in polynomial time by oracle transducers with oracle function ff. An oracle machine is equipped with an oracle query tape, ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, London, 1994.

....quantifiers. 2 Definition of the Quantifier In the following, we assume some familiarity of the reader with basic formal language theory (refer to the various articles in [RS97] basic complexity classes and resourcebounded reducibilities (refer to the standard literature, e.g. Pap94, BC94, BDG95] all complexity classes that appear in the present paper without definition are defined in [Joh90] as well as with the basics of finite model theory (refer to [Str94, EF95, Imm98] Given a language A over some alphabet Sigma, we denote the characteristic function of A by A , i.e. ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, London, 1994.

....set L is denoted by kLk. The characteristic function of a set L is denoted by c L , i.e. c L (x) 1 , x 2 L and c L (x) 0 , x = 2 L, for all x 2 . Let N = f0; 1; 2; g. For the basic notions of complexity theory such as P, NP, PSPACE, and so on see any standard text, e.g. [1, 19]. The computation model we use is the standard nondeterministic Turing machine. We review the de nitions of some complexity classes of functions, already existing in the literature, that we will use in this paper. FP denotes the class of all polynomial time computable, total functions from ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, New York, 1994.

....class we will see that finite automata as underlying model are essentially as good as polynomial time Turing machines. 2 Preliminaries We assume the reader is familiar with the basic automata and machine models from formal language theory and complexity theory, see, e.g. HU79, BDG95, BC94, Pap94] For more background on the models we use, we refer the reader to the different chapters in [RS97] Our Turing machines are standard multi tape machines, see [HU79] For the definition of sublinear time classes we use indexing machines, introduced in [Sip83] These machines cannot ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, London, 1994.

....to g almost everywhere, i.e. there is some n 0 such that for all n n 0 we have f(n) g(n) Let id denote the identity function given by id(n) def n for all n 2 N. We assume the reader to be familiar with basic complexity classes and reducibilities. Refer to the standard literature, e.g. [8, 26, 2]. Let FP be the class of total functions computed in polynomial time by deterministic Turing transducers. With FP we denote the class of functions computed in polynomial time by deterministic oracle Turing transducers with total oracle function . An oracle machine is equipped with an oracle ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, London, 1994.

....class we will see that finite automata as underlying model are essentially as good as polynomial time Turing machines. 2 Preliminaries We assume the reader is familiar with the basic automata and machine models from formal language theory and complexity theory, see, e.g. HU79, BDG95, BC94, Pap94] For more background on the models we use, we refer the reader to the different chapters in [RS97] Our Turing machines are standard multi tape machines, see [HU79] For the definition of sublinear time classes we use indexing machines, introduced in [Sip83] These machines cannot ....

D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, London, 1994.

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