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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 ..."
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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...
On the Complexity of SAT
, 1999
"... We show that nondeterministic time NT IME(n) is not contained in deterministic time n # 2# and polylogarithmic space, for any # > 0. This implies that (infinitely often) satisfiability cannot be solved in time O(n # 2# ) and polylogarithmic space. A similar result is presented for uniform circui ..."
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We show that nondeterministic time NT IME(n) is not contained in deterministic time n # 2# and polylogarithmic space, for any # > 0. This implies that (infinitely often) satisfiability cannot be solved in time O(n # 2# ) and polylogarithmic space. A similar result is presented for uniform circuits.
Optimal TimeSpace TradeOffs for Sorting
 In Proc. 39th IEEE Sympos. Found. Comput. Sci
, 1998
"... We study the fundamental problem of sorting in a sequential model of computation and in particular consider the timespace tradeoff (product of time and space) for this problem. ..."
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Cited by 10 (0 self)
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We study the fundamental problem of sorting in a sequential model of computation and in particular consider the timespace tradeoff (product of time and space) for this problem.
Machine Models and Linear Time Complexity
 SIGACT News
, 1993
"... wer bounds. Machine models. Suppose that for every machine M 1 in model M 1 running in time t = t(n) there is a machine M 2 in M 2 which computes the same partial function in time g = g(t; n). If g = O(t)+O(n) we say that model M 2 simulates M 1 linearly. If g = O(t) the simulation has constantf ..."
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Cited by 5 (3 self)
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wer bounds. Machine models. Suppose that for every machine M 1 in model M 1 running in time t = t(n) there is a machine M 2 in M 2 which computes the same partial function in time g = g(t; n). If g = O(t)+O(n) we say that model M 2 simulates M 1 linearly. If g = O(t) the simulation has constantfactor overhead ; if g = O(t log t) it has a factorofO(log t) overhead , and so on. The simulation is online if each step of M 1 i
Multiparty finite computations
 COCOON’99, Proc., LNCS 1627
, 1999
"... Abstract. We consider systems consisting of a finite number of finite automata which communicate by sending messages. We consider number of messages necessary to recognize a language as a complexity measure of the language. We feel that these considerations give a new insight into computational comp ..."
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Abstract. We consider systems consisting of a finite number of finite automata which communicate by sending messages. We consider number of messages necessary to recognize a language as a complexity measure of the language. We feel that these considerations give a new insight into computational complexity of problems computed by readonly devices in multiprocessor systems. Our considerations are related to multiparty communication complexity, but we make a realistic assumption that each party has a limited memory. We show a number of hierarchy results for this complexity measure: for each constant k there is a language, which may be recognized with k + 1 messages and cannot be recognized with k − 1 messages. We give an example of a language that requires Θ(log logn) messages and claim that Ω(loglog(n)) messages are necessary, if a language requires more than a constant number of messages. We present a language that requires Θ(n) messages. For a large family of functions f, f (n) = ω(loglogn), f (n) = o(n), we prove that there is a language which requires Θ ( f (n)) messages. Finally, we present functions that require ω(n) messages. 1
Communication Aspects of Computation of Systems of Finite Automata
, 2000
"... Many computing systems can be modeled by systems of cooperating finite automata. In fact, any existing physical device is finite, even... ..."
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Cited by 1 (1 self)
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Many computing systems can be modeled by systems of cooperating finite automata. In fact, any existing physical device is finite, even...
Aspekty Komunikacyjne Oblicze N Systemw Automatw Sko Nczonych
, 1999
"... port I would never be able to finish this thesis. I also thank my parents; they were always enthusiastic about my work. Contents 1 Introduction 1 1.1 Modes of Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Complexity Issues for Multiautomata Systems . . . . . . . ..."
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port I would never be able to finish this thesis. I also thank my parents; they were always enthusiastic about my work. Contents 1 Introduction 1 1.1 Modes of Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Complexity Issues for Multiautomata Systems . . . . . . . . . . . . . . . . . . 2 1.3 Notions and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.1 Multiautomata and Multiprocessors Systems . . . . . . . . . . . . . . . 4 1.3.2 Alternative Notion: Multihead and Multiprocessor Finite Automata. . 5 1.3.3 Communication Complexity . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.4 Communication Measure for Multiautomata Systems . . . . . . . . . . 6 1.3.5 Kolmogorov Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.6 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Previous Results . . . . . . . . . . . . . . . . . . . . . . . . . . . .
TimeSpace Tradeoffs for Set Operations
, 1994
"... This paper considers timespace tradeoffs for various set operations. Denoting the time requirement of an algorithm by T and its space requirement by S, it is shown that TS =\Omega (n 2 ) for set complementation and TS =\Omega \Gamma n 3=2 \Delta for set intersection, in the Rway branch ..."
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This paper considers timespace tradeoffs for various set operations. Denoting the time requirement of an algorithm by T and its space requirement by S, it is shown that TS =\Omega (n 2 ) for set complementation and TS =\Omega \Gamma n 3=2 \Delta for set intersection, in the Rway branching program model. In the more restricted model of comparison branching programs, the paper provides two additional types of results. A tradeoff of TS =\Omega \Gamma n 2\Gammaffl(n) \Delta , derived from Yao's lower bound for element distinctness, is shown for set disjointness, set union and set intersection (where ffl(n) = O \Gamma (log n) \Gamma1=2 \Delta ). A bound of TS =\Omega \Gamma n 3=2 \Delta is shown for deciding set equality and set inclusion. Finally, a classification of set operations is presented, and it is shown that all problems of a large naturally arising class are as hard as the problems bounded in this paper.
Rway Branching Programs and the Hamming Distance Problem
, 909
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS