11,925 research outputs found
More Structural Characterizations of Some Subregular Language Families by Biautomata
We study structural restrictions on biautomata such as, e.g., acyclicity,
permutation-freeness, strongly permutation-freeness, and orderability, to
mention a few. We compare the obtained language families with those induced by
deterministic finite automata with the same property. In some cases, it is
shown that there is no difference in characterization between deterministic
finite automata and biautomata as for the permutation-freeness, but there are
also other cases, where it makes a big difference whether one considers
deterministic finite automata or biautomata. This is, for instance, the case
when comparing strongly permutation-freeness, which results in the family of
definite language for deterministic finite automata, while biautomata induce
the family of finite and co-finite languages. The obtained results nicely fall
into the known landscape on classical language families.Comment: In Proceedings AFL 2014, arXiv:1405.527
On the interplay between Babai and Cerny's conjectures
Motivated by the Babai conjecture and the Cerny conjecture, we study the
reset thresholds of automata with the transition monoid equal to the full
monoid of transformations of the state set. For automata with states in
this class, we prove that the reset thresholds are upper-bounded by
and can attain the value . In addition, we study diameters
of the pair digraphs of permutation automata and construct -state
permutation automata with diameter .Comment: 21 pages version with full proof
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Permutation and sampling with maximum length CA for pseudorandom number generation
In this paper, we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata (CA). Dynamic permutation and sampling have not been explored in previous CA work and a suitable implementation is shown using a two CA model. Three different schemes that incorporate these two operations are suggested - Weighted Permutation Vector Sampling with Controlled Multiplexing, Weighted Permutation Vector Sampling with Irregular Decimation and Permutation Programmed CA Sampling. The experiment results show that the resulting sequences have varying degrees of improvement in DIEHARD results and linear complexity compared to the CA
Sweeping Permutation Automata
This paper introduces sweeping permutation automata, which move over an input
string in alternating left-to-right and right-to-left sweeps and have a
bijective transition function. It is proved that these automata recognize the
same family of languages as the classical one-way permutation automata
(Thierrin, "Permutation automata", Mathematical Systems Theory, 1968). An
n-state two-way permutation automaton is transformed to a one-way permutation
automaton with F(n)=\max_(k+l=n, m <= l) k (l \choose m) (k - 1 \choose l - m)
(l - m)! states. This number of states is proved to be necessary in the worst
case, and its growth rate is estimated as F(n) = n^(n/2 - (1 + \ln 2)/2 \cdot
n/(\ln n) \cdot (1 + o(1))).Comment: In Proceedings NCMA 2023, arXiv:2309.0733
On the interplay between Babai and Černý’s conjectures
Motivated by the Babai conjecture and the Černý conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with n states in this class, we prove that the reset thresholds are upperbounded by 2n2 -6n + 5 and can attain the value (Formula presented). In addition, we study diameters of the pair digraphs of permutation automata and construct n-state permutation automata with diameter (formula presented). © Springer International Publishing AG 2017
On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia
We construct a sequence of finite automata that accept subclasses of the
class of 4231-avoiding permutations. We thereby show that the Wilf-Stanley
limit for the class of 4231-avoiding permutations is bounded below by 9.35.
This bound shows that this class has the largest such limit among all classes
of permutations avoiding a single permutation of length 4 and refutes the
conjecture that the Wilf-Stanley limit of a class of permutations avoiding a
single permutation of length k cannot exceed (k-1)^2.Comment: Submitted to Advances in Applied Mathematic
Equivalence of DES and AES Algorithm with Cellular Automata
In this paper we present the equivalence of the operations involved in DES and AES algorithm with operations of cellular automata. We identify all the permutation and substitution operations involved in DES and AES algorithm and compare these operations with the cellular automata rules. Then we find that permutation operations involved in DES and AES are equivalent to linear cellular automata rules providing diffusion property of cryptography whereas substitution operations involved in DES and AES are equivalent to non linear cellular automata rules providing the confusion property of cryptography. Hence instead of using operations involved in DES and AES algorithm, we can apply linear as well as non-linear cellular automata rules in cryptography for better security and parallel processing
On random primitive sets, directable NDFAs and the generation of slowly synchronizing DFAs
We tackle the problem of the randomized generation of slowly synchronizing
deterministic automata (DFAs) by generating random primitive sets of matrices.
We show that when the randomized procedure is too simple the exponent of the
generated sets is O(n log n) with high probability, thus the procedure fails to
return DFAs with large reset threshold. We extend this result to random
nondeterministic automata (NDFAs) by showing, in particular, that a uniformly
sampled NDFA has both a 2-directing word and a 3-directing word of length O(n
log n) with high probability. We then present a more involved randomized
algorithm that manages to generate DFAs with large reset threshold and we
finally leverage this finding for exhibiting new families of DFAs with reset
threshold of order .Comment: 31 pages, 9 figures. arXiv admin note: text overlap with
arXiv:1805.0672
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