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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 ..."
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Cited by 35 (1 self)
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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 cir ..."
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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. Beame has ..."
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Cited by 13 (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. Beame has
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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Cited by 2 (1 self)
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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...
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.