289 research outputs found
Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the
state-complexity of representing sub- or superword closures of context-free
grammars (CFGs): (1) We prove a (tight) upper bound of on
the size of nondeterministic finite automata (NFAs) representing the subword
closure of a CFG of size . (2) We present a family of CFGs for which the
minimal deterministic finite automata representing their subword closure
matches the upper-bound of following from (1).
Furthermore, we prove that the inequivalence problem for NFAs representing sub-
or superword-closed languages is only NP-complete as opposed to PSPACE-complete
for general NFAs. Finally, we extend our results into an approximation method
to attack inequivalence problems for CFGs
New Deterministic Algorithms for Solving Parity Games
We study parity games in which one of the two players controls only a small
number of nodes and the other player controls the other nodes of the
game. Our main result is a fixed-parameter algorithm that solves bipartite
parity games in time , and general parity games in
time , where is the number of distinct
priorities and is the number of edges. For all games with this
improves the previously fastest algorithm by Jurdzi{\'n}ski, Paterson, and
Zwick (SICOMP 2008). We also obtain novel kernelization results and an improved
deterministic algorithm for graphs with small average degree
Fast Computation of Abelian Runs
Given a word and a Parikh vector , an abelian run of period
in is a maximal occurrence of a substring of having
abelian period . Our main result is an online algorithm that,
given a word of length over an alphabet of cardinality and a
Parikh vector , returns all the abelian runs of period
in in time and space , where is the
norm of , i.e., the sum of its components. We also present an
online algorithm that computes all the abelian runs with periods of norm in
in time , for any given norm . Finally, we give an -time
offline randomized algorithm for computing all the abelian runs of . Its
deterministic counterpart runs in time.Comment: To appear in Theoretical Computer Scienc
k-Abelian Pattern Matching
Two words are called -abelian equivalent, if they share the same multiplicities for all factors of length at most . We present an optimal linear time algorithm for identifying all occurrences of factors in a text that are -abelian equivalent to some pattern. Moreover, an optimal algorithm for finding the largest for which two words are -abelian equivalent is given. Solutions for various online versions of the -abelian pattern matching problem are also proposed
Design, Implementation and Experiments for Moving Target Defense Framework
The traditional defensive security strategy for distributed systems employs well-established defensive techniques such as; redundancy/replications, firewalls, and encryption to prevent attackers from taking control of the system. However, given sufficient time and resources, all these methods can be defeated, especially when dealing with sophisticated attacks from advanced adversaries that leverage zero-day exploits
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