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StateComplexity Hierarchies of Uniform Languages of AlphabetSize Length
, 2008
"... Abstract. We study the state complexity of certain simple languages. If A is an alphabet of k letters, then a klanguage is a nonempty set of words of length k, that is, a uniform language of length k. We show that the minimal state complexity of a klanguage is k+2 and the maximal, (kk−1−1)/(k−1)+2 ..."
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Abstract. We study the state complexity of certain simple languages. If A is an alphabet of k letters, then a klanguage is a nonempty set of words of length k, that is, a uniform language of length k. We show that the minimal state complexity of a klanguage is k+2 and the maximal, (kk−1−1)/(k−1
On the Average State and Transition Complexity of Finite Languages
, 2007
"... We investigate the averagecase state and transition complexity of deterministic and nondeterministic finite automata, when choosing a finite language of a certain “size” n uniformly at random from all finite languages of that particular size. Here size means that all words of the language are eithe ..."
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Cited by 6 (3 self)
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We investigate the averagecase state and transition complexity of deterministic and nondeterministic finite automata, when choosing a finite language of a certain “size” n uniformly at random from all finite languages of that particular size. Here size means that all words of the language
The Average State Complexity of Rational Operations on Finite Languages
, 2010
"... Considering the uniform distribution on sets of m nonempty words whose sum of lengths is n, we establish that the average state complexities of the rational operations are asymptotically linear. ..."
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Cited by 8 (2 self)
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Considering the uniform distribution on sets of m nonempty words whose sum of lengths is n, we establish that the average state complexities of the rational operations are asymptotically linear.
Materials for an exploratory theory of the network society.
 The British Journal of Sociology
, 2000
"... ABSTRACT This article aims at proposing some elements for a grounded theor y of the network society. The network society is the social structure characteristic of the Information Age, as tentatively identi ed by empirical, crosscultural investigation. It permeates most societies in the world, in v ..."
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Cited by 122 (0 self)
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witnessing a proliferation of in uential, resourceful nongovernmental organizations that interact with governments, and multinational political institutions. Thus, overall the new state is not any longer a nationstate. The state in the information age is a network state, a state made out of a complex web
HyperPolynomial Hierarchies and the NPJump
"... Assuming that the polynomial hierarchy (PH) does not collapse, we show the existence of ascending sequences of ptime Turing degrees of length ! CK 1 all of which are in PSPACE and uniformly hard for PH, such that successors are NPjumps of their predecessors. This is analgous to the hyperarithm ..."
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Assuming that the polynomial hierarchy (PH) does not collapse, we show the existence of ascending sequences of ptime Turing degrees of length ! CK 1 all of which are in PSPACE and uniformly hard for PH, such that successors are NPjumps of their predecessors. This is analgous
A Clarification Concerning the #L Hierarchy
, 1997
"... In [AO96], it is stated (without proof) that if NC 1 (#L) = AC 0 (#L), then the #L hierarchy collapses to some level. This note provides a proof of that claim. The reader is referred to [AO96] for all background, definitions, and motivation. All of the circuit complexity classes mentioned in thi ..."
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Cited by 2 (0 self)
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In [AO96], it is stated (without proof) that if NC 1 (#L) = AC 0 (#L), then the #L hierarchy collapses to some level. This note provides a proof of that claim. The reader is referred to [AO96] for all background, definitions, and motivation. All of the circuit complexity classes mentioned
HyperPolynomial Hierarchies and the NPJump
"... Assuming that the polynomial hierarchy (PH) does not collapse, we show the existence of ascending sequences of ptime Turing degrees of length ! CK 1 all of which are in PSPACE and uniformly hard for PH, such that successors are NPjumps of their predecessors. This is analgous to the hyperarithm ..."
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Assuming that the polynomial hierarchy (PH) does not collapse, we show the existence of ascending sequences of ptime Turing degrees of length ! CK 1 all of which are in PSPACE and uniformly hard for PH, such that successors are NPjumps of their predecessors. This is analgous
The average state complexity of the star of a ﬁnite set of words is linear
"... We prove that, for the uniform distribution over all sets X
of m (that is a ﬁxed integer) nonempty words whose sum of lengths is
n, D_X , one of the usual deterministic automata recognizing X^∗ , has on
average O(n) states and that the average state complexity of X^∗ is Θ(n).
We also show that the ..."
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We prove that, for the uniform distribution over all sets X
of m (that is a ﬁxed integer) nonempty words whose sum of lengths is
n, D_X , one of the usual deterministic automata recognizing X^∗ , has on
average O(n) states and that the average state complexity of X^∗ is Θ(n).
We also show
Monoids and the state complexity of the operation root(L
, 2003
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii In this thesis, we cover the general topic of state co ..."
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and regular expressions. This includes an improvement on the worstcase lower bound for a regular expression, relative to its alphabetic length. The focus of this thesis is the study of the increase in state complexity of a regular language L under the operation root(L). This operation requires us to examine
Results 1  10
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129