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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...
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . .