260 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
Cooperating Distributed Grammar Systems of Finite Index Working in Hybrid Modes
We study cooperating distributed grammar systems working in hybrid modes in
connection with the finite index restriction in two different ways: firstly, we
investigate cooperating distributed grammar systems working in hybrid modes
which characterize programmed grammars with the finite index restriction;
looking at the number of components of such systems, we obtain surprisingly
rich lattice structures for the inclusion relations between the corresponding
language families. Secondly, we impose the finite index restriction on
cooperating distributed grammar systems working in hybrid modes themselves,
which leads us to new characterizations of programmed grammars of finite index.Comment: In Proceedings AFL 2014, arXiv:1405.527
Alternating and empty alternating auxiliary stack automata
AbstractWe consider variants of alternating auxiliary stack automata and characterize their computational power when the number of alternations is bounded by a constant or unlimited. In this way we get new characterizations of NP, the polynomial hierarchy, PSpace, and bounded query classes like co-DP=NL〈NP[1]〉 and Θ2P=PNP[O(logn)], in a uniform framework
Optimal Regular Expressions for Palindromes of Given Length
The language P_n (P?_n, respectively) consists of all words that are palindromes of length 2n (2n-1, respectively) over a fixed binary alphabet. We construct a regular expression that specifies P_n (P?_n, respectively) of alphabetic width 4? 2?-4 (3? 2?-4, respectively) and show that this is optimal, that is, the expression has minimum alphabetic width among all expressions that describe P_n (P?_n, respectively). To this end we give optimal expressions for the first k palindromes in lexicographic order of odd and even length, proving that the optimal bound is 2n+4(k-1)-2 S?(k-1) in case of odd length and 2n+3(k-1)-2 S?(k-1)-1 for even length, respectively. Here S?(n) refers to the Hamming weight function, which denotes the number of ones in the binary expansion of the number n
On Minimal Pumping Constants for Regular Languages
The study of the operational complexity of minimal pumping constants started
in [J. DASSOW and I. JECKER. Operational complexity and pumping lemmas. Acta
Inform., 59:337-355, 2022], where an almost complete picture of the operational
complexity of minimal pumping constants for two different variants of pumping
lemmata from the literature was given. We continue this research by considering
a pumping lemma for regular languages that allows pumping of sub-words at any
position of the considered word, if the sub-word is long enough [S. J. SAVITCH.
Abstract Machines and Grammars. 1982]. First we improve on the simultaneous
regulation of minimal pumping constants induced by different pumping lemmata
including Savitch's pumping lemma. In this way we are able to simultaneously
regulate four different minimal pumping constants. This is a novel result in
the field of descriptional complexity. Moreover, for Savitch's pumping lemma we
are able to completely classify the range of the minimal pumping constant for
the operations Kleene star, reversal, complement, prefix- and suffix-closure,
union, set-subtraction, concatenation, intersection, and symmetric difference.
In this way, we also solve some of the open problems from the paper that
initiated the study of the operational complexity of minimal pumping constants
mentioned above.Comment: In Proceedings AFL 2023, arXiv:2309.0112
Advanced Automatic Code Generation for Multiple Relaxation-Time Lattice Boltzmann Methods
The scientific code generation package lbmpy supports the automated design
and the efficient implementation of lattice Boltzmann methods (LBMs) through
metaprogramming. It is based on a new, concise calculus for describing multiple
relaxation-time LBMs, including techniques that enable the numerically
advantageous subtraction of the constant background component from the
populations. These techniques are generalized to a wide range of collision
spaces and equilibrium distributions. The article contains an overview of
lbmpy's front-end and its code generation pipeline, which implements the new
LBM calculus by means of symbolic formula manipulation tools and
object-oriented programming. The generated codes have only a minimal number of
arithmetic operations. Their automatic derivation rests on two novel Chimera
transforms that have been specifically developed for efficiently computing raw
and central moments. Information contained in the symbolic representation of
the methods is further exploited in a customized sequence of algebraic
simplifications, further reducing computational cost. When combined, these
algebraic transformations lead to concise and compact numerical kernels.
Specifically, with these optimizations, the advanced central moment- and
cumulant-based methods can be realized with only little additional cost as when
compared with the simple BGK method. The effectiveness and flexibility of the
new lbmpy code generation system is demonstrated in simulating Taylor-Green
vortex decay and the automatic derivation of an LBM algorithm to solve the
shallow water equations.Comment: 23 pages, 6 figure
Preface: 11th Workshop on Non-classical Models of Automata and Applications (NCMA 2019)
Holzer, M.; Sempere Luna, JM. (2021). Preface: 11th Workshop on Non-classical Models of Automata and Applications (NCMA 2019). RAIRO - Theoretical Informatics and Applications. 55:1-2. https://doi.org/10.1051/ita/2021009S125
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