Results 1  10
of
13
TimeSpace Tradeoffs for Satisfiability
 Journal of Computer and System Sciences
, 1997
"... We give the first nontrivial modelindependent timespace tradeoffs for satisfiability. Namely, we show that SAT cannot be solved simultaneously in n 1+o(1) time and n 1\Gammaffl space for any ffl ? 0 on general randomaccess nondeterministic Turing machines. In particular, SAT cannot be solved ..."
Abstract

Cited by 29 (1 self)
 Add to MetaCart
We give the first nontrivial modelindependent timespace tradeoffs for satisfiability. Namely, we show that SAT cannot be solved simultaneously in n 1+o(1) time and n 1\Gammaffl space for any ffl ? 0 on general randomaccess nondeterministic Turing machines. In particular, SAT cannot be solved deterministically by a Turing machine using quasilinear time and p n space. We also give lower bounds for logspace uniform NC 1 circuits and branching programs. Our proof uses two basic ideas. First we show that if SAT can be solved nondeterministically with a small amount of time then we can collapse a nonconstant number of levels of the polynomialtime hierarchy. We combine this work with a result of Nepomnjascii that shows that a nondeterministic computation of super linear time and sublinear space can be simulated in alternating linear time. A simple diagonalization yields our main result. We discuss how these bounds lead to a new approach to separating the complexity classes NL a...
The complexity of propositional proofs
 Bulletin of Symbolic Logic
"... Abstract. Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorit ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
Abstract. Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorithms. This is article includes a broad survey of the field, and a technical exposition of some recently developed techniques for proving lower bounds on proof sizes. Contents
Rudimentary Reductions Revisited
 Information Processing Letters 40
, 1991
"... We show that logbounded rudimentary reductions #de#ned and studied by Jones in 1975# characterize Dlogtimeuniform AC . ..."
Abstract

Cited by 18 (9 self)
 Add to MetaCart
We show that logbounded rudimentary reductions #de#ned and studied by Jones in 1975# characterize Dlogtimeuniform AC .
First Order Logic, Fixed Point Logic and Linear Order
, 1995
"... The Ordered conjecture of Kolaitis and Vardi asks whether fixedpoint logic differs from firstorder logic on every infinite class of finite ordered structures. In this paper, we develop the tool of bounded variable element types, and illustrate its application to this and the original conjectures o ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
The Ordered conjecture of Kolaitis and Vardi asks whether fixedpoint logic differs from firstorder logic on every infinite class of finite ordered structures. In this paper, we develop the tool of bounded variable element types, and illustrate its application to this and the original conjectures of McColm, which arose from the study of inductive definability and infinitary logic on proficient classes of finite structures (those admitting an unbounded induction). In particular, for a class of finite structures, we introduce a compactness notion which yields a new proof of a ramified version of McColm's second conjecture. Furthermore, we show a connection between a modeltheoretic preservation property and the Ordered Conjecture, allowing us to prove it for classes of strings (colored orderings). We also elaborate on complexitytheoretic implications of this line of research.
Complexity Doctrines
, 1995
"... vii Introduction ix 1 Tensor and Linear Time 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.1 Almost Equational Specification : : : : : : : : : : : : : : : : : 3 1.1.1 Sketches : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.1.2 Orthogonality : : : : : : : : : : ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
vii Introduction ix 1 Tensor and Linear Time 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.1 Almost Equational Specification : : : : : : : : : : : : : : : : : 3 1.1.1 Sketches : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.1.2 Orthogonality : : : : : : : : : : : : : : : : : : : : : : : 5 1.1.3 Essentially Algebraic Specification : : : : : : : : : : : : 8 1.2 Tensor and System T : : : : : : : : : : : : : : : : : : : : : : : 10 1.2.1 Serial Composition : : : : : : : : : : : : : : : : : : : : 10 1.2.2 Parallel Composition : : : : : : : : : : : : : : : : : : : 11 1.2.3 Unary Numbers : : : : : : : : : : : : : : : : : : : : : : 13 1.2.4 System T : : : : : : : : : : : : : : : : : : : : : : : : : 13 1.3 Comprehensions and Tiers : : : : : : : : : : : : : : : : : : : : 15 1.3.1 Comprehensions : : : : : : : : : : : : : : : : : : : : : : 15 1.3.2 Extents : : : : : : : : : : : : : : : : : : : : : : : : : : 18 1.3.3 Dyadic Numbers : : : : : : : : : : : : : : : ...
On Quasilinear Time Complexity Theory
, 1994
"... This paper furthers the study of quasilinear time complexity initiated by Schnorr and Gurevich and Shelah. We show that the fundamental properties of the polynomialtime hierarchy carry over to the quasilineartime hierarchy. ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
This paper furthers the study of quasilinear time complexity initiated by Schnorr and Gurevich and Shelah. We show that the fundamental properties of the polynomialtime hierarchy carry over to the quasilineartime hierarchy.
The Descriptive Complexity of the FixedPoints of Bounded Formulas
 Computer Science Logic '2000, 14th Annual Conference of the EACSL, volume 1862 of Lecture Notes in Computer Science
, 2000
"... . We investigate the complexity of the fixedpoints of bounded formulas in the context of finite set theory; that is, in the context of arbitrary classes of finite structures that are equipped with a builtin BIT predicate, or equivalently, with a builtin membership relation between hereditaril ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
. We investigate the complexity of the fixedpoints of bounded formulas in the context of finite set theory; that is, in the context of arbitrary classes of finite structures that are equipped with a builtin BIT predicate, or equivalently, with a builtin membership relation between hereditarily finite sets (input relations are allowed). We show that the iteration of a positive bounded formula converges in polylogarithmically many steps in the cardinality of the structure. This extends a previously known much weaker result. We obtain a number of connections with the rudimentary languages and deterministic polynomialtime. Moreover, our results provide a natural characterization of the complexity class consisting of all languages computable by boundeddepth, polynomialsize circuits, and polylogarithmictime uniformity. As a byproduct, we see that this class coincides with LH(P), the logarithmictime hierarchy with an oracle to deterministic polynomialtime. Finally, we dis...
A Predicative and Decidable Characterization of the Polynomial Classes of Languages
"... The definition of a class C of functions is predicative if it doesn't use a class containing C; and is decidable if membership to C can be decided syntactically, from the construction of its elements. Decidable and predicative characterizations of Polytime functions are known. We present here such ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
The definition of a class C of functions is predicative if it doesn't use a class containing C; and is decidable if membership to C can be decided syntactically, from the construction of its elements. Decidable and predicative characterizations of Polytime functions are known. We present here such a characterization for the following classes of languages : P, \Sigma p n ; \Delta p n , PH and PSPACE. It is obtained by means of a progressive sequence of restrictions to recursion in a dialect of Lisp. 1 Introduction The impredicativity [ 12 ] of defining a complexity class C by means of TM's plus clocks or meters has been pointedout by Leivant [ 8 ]. Moreover, studying C in terms of operators, instead of resources, may help understanding its inner nature. To this purpose, several predicative definitions by closure under different kinds of limited recursion have been suggested. Somehow in the spirit of the Grzegorczyk classes, these partial operators are restrictions R of other...