On the Power of Las Vegas for One-Way Communication Complexity, OBDDs, and Finite Automata

Hromkovič, Juraj; Schnitger, Georg

doi:10.1006/inco.2001.3040

Cited by 44 publications

(41 citation statements)

References 20 publications

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“…For a concrete example of a uniform one-way protocol one can look at [24,1]. Interestingly, for each regular language L, the message complexity of deterministic uniform one-way protocols accepting L equals the size of the minimal deterministic finite automaton for L. To see this fact one has to represent the task of accepting L as the infinite communication matrix M L for L (Fig.…”

Section: Communication Complexity and Proving Lower Bounds On The Sizmentioning

confidence: 99%

“…Another example is the finite language L n = {0 2n xx | x ∈ {0, 1} n }, whose deterministic message complexity is 2, but the size of the minimal NFA's is at least 2 n . In order to overcome this drawback we have introduced uniform one-way protocols in [24]. A uniform one-way protocol (C 1 , C 2 ) consists again of two computers C 1 and C 2 , but inputs x = x 1 , x 2 , .…”

Section: Communication Complexity and Proving Lower Bounds On The Sizmentioning

confidence: 99%

“…In Section 2 we introduce two-party communication protocols of Yao [34] and show that the one-way version of them is related to finite automata [23,19]. Then we extend one-way two-party protocols to a uniform computing model [24], and show that their communication complexity provide lower bounds that are at least as good as the lower bounds provided by the fooling method [11,6] or the geometrical approach [8].…”

Section: Introductionmentioning

confidence: 98%

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On the limits of the communication complexity technique for proving lower bounds on the size of minimal NFA’s

Hromkovi

Petersen

Schnitger

2009

Theoretical Computer Science

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a b s t r a c tIn contrast to the minimization of deterministic finite automata (DFA's), the task of constructing a minimal nondeterministic finite automaton (NFA) for a given NFA is PSPACEcomplete. Moreover, there are no polynomial approximation algorithms with a constant approximation ratio for estimating the number of states of minimal NFA's.Since one is unable to efficiently estimate the size of a minimal NFA in an efficient way, one should ask at least for developing mathematical proof methods that help to prove good lower bounds on the size of a minimal NFA for a given regular language. Here we consider the robust and most successful lower bound proof technique that is based on communication complexity. In this paper it is proved that even a strong generalization of this method fails for some concrete regular languages.''To fail'' is considered here in a very strong sense. There is an exponential gap between the size of a minimal NFA and the achievable lower bound for a specific sequence of regular languages.The generalization of the concept of communication protocols is also strong here.It is shown that cutting the input word into 2 O(n 1/4 ) pieces for a size n of a minimal nondeterministic finite automaton and investigating the necessary communication transfer between these pieces as parties of a multiparty protocol does not suffice to get good lower bounds on the size of minimal nondeterministic automata. It seems that for some regular languages one cannot really abstract from the automata model that cuts the input words into particular symbols of the alphabet and reads them one by one using its input head.

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Section: Communication Complexity and Proving Lower Bounds On The Sizmentioning

confidence: 99%

Section: Communication Complexity and Proving Lower Bounds On The Sizmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

On the limits of the communication complexity technique for proving lower bounds on the size of minimal NFA’s

Hromkovi

Petersen

Schnitger

2009

Theoretical Computer Science

Self Cite

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“…Before doing this, let us begin with a general construction, converting two given NFAs A + and A − , accepting a language L and its complement L c , respectively, into equivalent SVFA A for L. As pointed out in [6], A can be obtained by introducing a new initial state, connected to copies of A + and A − with suitable transitions. The total number of the states in A is thus the sum of the corresponding numbers in the two original automata, plus 1.…”

Section: The Superpolynomial Gapmentioning

confidence: 99%

Pairs of Complementary Unary Languages with “Balanced” Nondeterministic Automata

Geffert

Pighizzini

2010

Algorithmica

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For each sufficiently large n, there exists a unary regular language L such that both L and its complement L c are accepted by unambiguous nondeterministic automata with at most n states, while the smallest deterministic automata for these two languages still require a superpolynomial number of states, at least e ( 3 √ n·ln 2 n) . Actually, L and L c are "balanced" not only in the number of states but, moreover, they are accepted by nondeterministic machines sharing the same transition graph, differing only in the distribution of their final states. As a consequence, the gap between the sizes of unary unambiguous self-verifying automata and deterministic automata is also superpolynomial.

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“…Because of the enormous hardness of this problem many researchers try to separate determinism from randomization and randomization from nondeterminism at least for restricted models of computations (see, for instance, [2][3][4][5][6][7][9][10][11][12][13]15,[17][18][19]21,[23][24][25]) in order to gain further insight into the computational power of these modes of computation.…”

Section: Introductionmentioning

confidence: 99%

On the power of randomized multicounter machines

Hromkovič

Schnitger

2005

Theoretical Computer Science

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One-way two-counter machines represent a universal model of computation. Here we consider the polynomial-time classes of multicounter machines with a constant number of reversals and separate the computational power of nondeterminism, randomization and determinism. For instance, we show that polynomial-time one-way multicounter machines, with error probability tending to zero with growing input length, can recognize languages that cannot be accepted by polynomial-time nondeterministic two-way multicounter machines with a bounded number of reversals. A similar result holds for the comparison of determinism and one-sided-error randomization, and of determinism and Las Vegas randomization.

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On the Power of Las Vegas for One-Way Communication Complexity, OBDDs, and Finite Automata

Cited by 44 publications

References 20 publications

On the limits of the communication complexity technique for proving lower bounds on the size of minimal NFA’s

On the limits of the communication complexity technique for proving lower bounds on the size of minimal NFA’s

Pairs of Complementary Unary Languages with “Balanced” Nondeterministic Automata

On the power of randomized multicounter machines

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