scholarly journals BERGMAN under MS-DOS and Anick's resolution

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
S. Cojocaru ◽  
V. Ufnarovski
Keyword(s):  
Hilbert Series ◽  
The Other ◽  
Finite State Automata ◽  
Universal Enveloping Algebras ◽  
Generators And Relations ◽  
Enveloping Algebras ◽  
Finite State ◽  
Algorithmic Problems ◽  
Noncommutative Algebras ◽  
International Audience

International audience Noncommutative algebras, defined by the generators and relations, are considered. The definition and main results connected with the Gröbner basis, Hilbert series and Anick's resolution are formulated. Most attention is paid to universal enveloping algebras. Four main examples illustrate the main concepts and ideas. Algorithmic problems arising in the calculation of the Hilbert series are investigated. The existence of finite state automata, defining thebehaviour of the Hilbert series, is discussed. The extensions of the BERGMAN package for IBM PC compatible computers are described. A table is provided permitting a comparison of the effectiveness of the calculations in BERGMAN with the other systems.

scholarly journals Copyful Streaming String Transducers

2021 ◽  
Vol 178 (1-2) ◽  
pp. 59-76
Author(s):  
Emmanuel Filiot ◽  
Pierre-Alain Reynier
Keyword(s):  
Polynomial Time ◽  
Equivalence Problem ◽  
Expressive Power ◽  
The Other ◽  
Finite State Automata ◽  
Finite State ◽  
Variable Content ◽  
Deterministic Automata ◽  
Intermediate Output ◽  
Linear Manner

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Černý in 2010 as a one-way deterministic automata model to define transductions of finite strings. Copyless SST extend deterministic finite state automata with a set of variables in which to store intermediate output strings, and those variables can be combined and updated all along the run, in a linear manner, i.e., no variable content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string transductions, and are as expressive as deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decidable equivalence problem (in PSpace). On the other hand, HDT0L systems have been introduced for a while, the most prominent result being the decidability of the equivalence problem. In this paper, we propose a semantics of HDT0L systems in terms of transductions, and use it to study the class of deterministic copyful SST. Our contributions are as follows: (i)HDT0L systems and total deterministic copyful SST have the same expressive power, (ii)the equivalence problem for deterministic copyful SST and the equivalence problem for HDT0L systems are inter-reducible, in quadratic time. As a consequence, equivalence of deterministic SST is decidable, (iii)the functionality of non-deterministic copyful SST is decidable, (iv)determining whether a non-deterministic copyful SST can be transformed into an equivalent non-deterministic copyless SST is decidable in polynomial time.

Tricolor automata

2015 ◽  
Author(s):  
C. M. Sperberg-McQueen
Keyword(s):  
Regular Languages ◽  
The Other ◽  
Finite State Automata ◽  
Simple Application ◽  
Finite State

Tricolor automata are extensions of finite state automata, intended for the comparison of two regular languages; states and arcs in the automaton are colored to indicate whether they are peculiar to one language or the other, or common to both. Their design represents a simple application to practical purposes of ideas derived from the work of Glushkov and Brzozowski. Examples are given to show how tricolor automata can be used to visualize the intersection, union, and set difference of two languages, and algorithms for constructing them are given.

scholarly journals Applications of the finite state automata for counting restricted permutations and variations

2012 ◽  
Vol 22 (2) ◽  
pp. 183-198
Author(s):  
Vladimir Baltic
Keyword(s):  
The Other ◽  
Finite State Automaton ◽  
Finite State Automata ◽  
Combinatorial Structures ◽  
Restricted Permutations ◽  
Finite State

In this paper, we use the finite state automata to count the number of restricted permutations and the number of restricted variations. For each type of restricted permutations, we construct a finite state automaton able to recognize and enumerate them. We, also, discuss how it encompasses the other known methods for enumerating permutations with restricted position, and in one case, we establish connections with some other combinatorial structures, such as subsets and compositions.

scholarly journals Hopcroft's automaton minimization algorithm and Sturmian words

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Jean Berstel ◽  
Luc Boasson ◽  
Olivier Carton
Keyword(s):  
Finite State Automata ◽  
Minimization Algorithm ◽  
Worst Case ◽  
Finite State ◽  
International Audience ◽  
Sturmian Words ◽  
Worst Case Behavior

International audience This paper is concerned with the analysis of the worst case behavior of Hopcroft's algorithm for minimizing deterministic finite state automata. We extend a result of Castiglione, Restivo and Sciortino. They show that Hopcroft's algorithm has a worst case behavior for the automata recognizing Fibonacci words. We prove that the same holds for all standard Sturmian words having an ultimately periodic directive sequence (the directive sequence for Fibonacci words is $(1,1,\ldots)$).

scholarly journals Comments on “Incremental Construction and Maintenance of Minimal Finite-State Automata,” by Rafael C. Carrasco and Mikel L. Forcada

2004 ◽  
Vol 30 (2) ◽  
pp. 227-235 ◽  
Author(s):  
Jan Daciuk
Keyword(s):  
Recent Article ◽  
The Other ◽  
Finite State Automata ◽  
Incremental Algorithms ◽  
Finite State ◽  
Incremental Construction ◽  
Cyclic Automaton ◽  
Incremental Addition

In a recent article, Carrasco and Forcada (June 2002) presented two algorithms: one for incremental addition of strings to the language of a minimal, deterministic, cyclic automaton, and one for incremental removal of strings from the automaton. The first algorithm is a generalization of the “algorithm for unsorted data”—the second of the two incremental algorithms for construction of minimal, deterministic, acyclic automata presented in Daciuk et al. (2000). We show that the other algorithm in the older article—the “algorithm for sorted data”—can be generalized in a similar way. The new algorithm is faster than the algorithm for addition of strings presented in Carrasco and Forcada's article, as it handles each state only once.

scholarly journals PBW Property for Associative Universal Enveloping Algebras Over an Operad

2020 ◽  
Author(s):  
Anton Khoroshkin
Keyword(s):  
Associative Algebra ◽  
Hilbert Series ◽  
Abelian Category ◽  
Universal Enveloping Algebra ◽  
Necessary Condition ◽  
Grobner Basis ◽  
Universal Enveloping Algebras ◽  
Enveloping Algebras ◽  
Enveloping Algebra ◽  
Category Of Modules

Abstract Given a symmetric operad $\mathcal{P}$ and a $\mathcal{P}$-algebra $V$, the associative universal enveloping algebra ${\textsf{U}_{\mathcal{P}}}$ is an associative algebra whose category of modules is isomorphic to the abelian category of $V$-modules. We study the notion of PBW property for universal enveloping algebras over an operad. In case $\mathcal{P}$ is Koszul a criterion for the PBW property is found. A necessary condition on the Hilbert series for $\mathcal{P}$ is discovered. Moreover, given any symmetric operad $\mathcal{P}$, together with a Gröbner basis $G$, a condition is given in terms of the structure of the underlying trees associated with leading monomials of $G$, sufficient for the PBW property to hold. Examples are provided.

scholarly journals Michelangelo, the Duck and the Rabbit

2021 ◽  
Vol 9 (2) ◽  
pp. 1-29
Author(s):  
Juan Felipe Miranda Medina ◽  
Marisol Cristel Galarza Flores
Keyword(s):  
Computer Science ◽  
The Other ◽  
Finite State Automata ◽  
Finite State ◽  
Modes Of Existence ◽  
Narrative Account ◽  
Virtual Mode

The concept of modes of existence of semiotic entities underlies (post)Greimasian semiotics, yet it seems to have received little attention. Modes of existence can be used in different senses. For Greimas, from the perspective of narrative semiotics, when Michelangelo first receives a block of marble and decides to sculpt the David, his intention is in a virtual mode; as Michelangelo progresses he ends up bringing the David into existence, and his intention comes to the realized mode. In Fontanille’s tensive semiotics, however, modes of existence can have to do with how one can narrow or broaden the scope of our apprehension of the David as our eyes look at it in order to produce a meaningful experience. In this work, the perspectives of narrative and tensive semiotics are contrasted both theoretically and practically applying both to a number of examples. In order to identify all possible modes of existence and all the possibilities of transitioning from one to the other in the examples presented, we resort to the method of finite-state automata from computer science. In the end, we propose a robust narrative account of modes of existence that relies on narrative semiotics for its definition, but into which intent and apprehension from tensive semiotics can be integrated. This work calls for the need of establishing a syntax of modes of existence, since both Greimas and Fontanille construe them as being necessary to account for the production of signification.

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