scholarly journals Infinitely generated semigroups and polynomial complexity

2016 ◽  
Vol 26 (04) ◽  
pp. 727-750 ◽  
Author(s):  
J. C. Birget
Keyword(s):  
Polynomial Time ◽  
Time Complexity ◽  
Polynomial Complexity ◽  
Free Monoid ◽  
Functional Approach ◽  
Finitely Generated ◽  
Machine Model ◽  
Polynomial Time Complexity ◽  
Evaluation Functions ◽  
Separation Results

This paper continues the functional approach to the [Formula: see text]-vs.-[Formula: see text] problem, begun in [J. C. Birget, Semigroups and one-way functions, Internat. J. Algebra Comput. 25 (1–2) (2015) 3–36]. Here, we focus on the monoid [Formula: see text] of right-ideal morphisms of the free monoid, that have polynomial input balance and polynomial time-complexity. We construct a machine model for the functions in [Formula: see text], and evaluation functions. We prove that, [Formula: see text] is not finitely generated, and use this to show separation results for time-complexity.

scholarly journals Polynomial-time right-ideal morphisms and congruences

2018 ◽  
Vol 28 (05) ◽  
pp. 791-835 ◽  
Author(s):  
J. C. Birget
Keyword(s):  
Homomorphic Image ◽  
Polynomial Time ◽  
Polynomial Complexity ◽  
Functional Approach ◽  
Finitely Generated ◽  
Group Of Units ◽  
Np Problem ◽  
Thompson Group

We continue with the functional approach to the P -versus- NP problem, begun in [J. C. Birget, Semigroups and one-way functions, Int. J. Algebra Comput. 25(1–2) (2015) 3–36; J. C. Birget, Infinitely generated semigroups and polynomial complexity, Int. J. Algebra Comput. 26(04) (2016) 727–750.] We previously constructed a monoid [Formula: see text] that is non-regular iff NP [Formula: see text] P . We now construct homomorphic images of [Formula: see text] with interesting properties. In particular, the homomorphic image [Formula: see text] of [Formula: see text] is finitely generated, and is non-regular iff P [Formula: see text] NP . The group of units of [Formula: see text] is the famous Richard Thompson group [Formula: see text].

COUNTING NUMERICAL SEMIGROUPS WITH SHORT GENERATING FUNCTIONS

2011 ◽  
Vol 21 (07) ◽  
pp. 1217-1235 ◽  
Author(s):  
VÍCTOR BLANCO ◽  
PEDRO A. GARCÍA-SÁNCHEZ ◽  
JUSTO PUERTO
Keyword(s):  
Generating Function ◽  
Polynomial Time ◽  
Generating Functions ◽  
Time Complexity ◽  
Frobenius Number ◽  
Numerical Semigroups ◽  
Polynomial Time Complexity ◽  
Theoretical Results

This paper presents a new methodology to compute the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron that classifies the semigroups with given genus (or Frobenius number) and multiplicity. First, we give theoretical results about the polynomial-time complexity of counting these semigroups. We also illustrate the methodology analyzing the cases of multiplicity 3 and 4 where some formulas for the number of numerical semigroups for any genus and Frobenius number are obtained.

scholarly journals ON THE EDGE OF DECIDABILITY IN COMPLEXITY ANALYSIS OF LOOP PROGRAMS

2012 ◽  
Vol 23 (07) ◽  
pp. 1451-1464 ◽  
Author(s):  
AMIR M. BEN-AMRAM ◽  
LARS KRISTIANSEN
Keyword(s):  
Second Language ◽  
Programming Language ◽  
Polynomial Time ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Feasibility Problem ◽  
Polynomial Time Complexity ◽  
Turing Complete ◽  
The Given

We investigate the decidability of the feasibility problem for imperative programs with bounded loops. A program is called feasible if all values it computes are polynomially bounded in terms of the input. The feasibility problem is representative of a group of related properties, like that of polynomial time complexity. It is well known that such properties are undecidable for a Turing-complete programming language. They may be decidable, however, for languages that are not Turing-complete. But if these languages are expressive enough, they do pose a challenge for analysis. We are interested in tracing the edge of decidability for the feasibility problem and similar problems. In previous work, we proved that such problems are decidable for a language where loops are bounded but indefinite (that is, the loops may exit before completing the given iteration count). In this paper, we consider definite loops. A second language feature that we vary, is the kind of assignment statements. With ordinary assignment, we prove undecidability of a very tiny language fragment. We also prove undecidability with lossy assignment (that is, assignments where the modified variable may receive any value bounded by the given expression, even zero). But we prove decidability with max assignments (that is, assignments where the modified variable never decreases its value).

A Polynomial Function Discovery System — FFS

1997 ◽  
Vol 06 (01) ◽  
pp. 1-13
Author(s):  
Spyros Tzafestas ◽  
Zhifang Ma
Keyword(s):  
Polynomial Time ◽  
Time Complexity ◽  
Polynomial Function ◽  
Polynomial Time Complexity ◽  
Discovery System ◽  
Function Discovery

This paper presents a function discovery system FFS that has two core parts: FFS-0-CORE and FFS-1-CORE. Both cores are with polynomial time complexity in discovering functions of either a•f(x)+b form or a1f1(x)+…+anfn(x)+b form. FFS-0-CORE allows users to define their own models. FFS-1-CORE uses novel principles to increase information which helps the function discovery procedures. Three computational examples are included.

scholarly journals Grammatical inference of directed acyclic graph languages with polynomial time complexity

2018 ◽  
Vol 95 ◽  
pp. 19-34
Author(s):  
Antonio-Javier Gallego ◽  
Damián López ◽  
Jorge Calera-Rubio
Keyword(s):  
Polynomial Time ◽  
Time Complexity ◽  
Directed Acyclic Graph ◽  
Grammatical Inference ◽  
Acyclic Graph ◽  
Polynomial Time Complexity ◽  
Graph Languages
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