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New formal language theory concepts introduced for factorization and presentation

By PulseAugur Editorial · [1 sources] ·

Researchers have introduced new concepts in formal language theory, focusing on relative prime factorization and finite-state presentations within specific algebraic structures. They differentiate between unique factorization and the finite relative presentation property (FRP), demonstrating that a finite quotient can have unique factorization without possessing FRP. To address this, they propose the finite-state relative presentation property (FSRP) and prime-target left-division determinism (PTLD), which implies unique factorization and other desirable properties. The work also includes a learning algorithm for canonical PTLD presentations. AI

RANK_REASON The cluster contains a research paper published on arXiv detailing theoretical computer science concepts. [lever_c_demoted from research: ic=1 ai=0.4]

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New formal language theory concepts introduced for factorization and presentation

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The cluster contains a research paper published on arXiv detailing theoretical computer science concepts. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Takayuki Kuriyama ·

    Relative Prime Factorization and Finite-State Presentations under Fixed Finite-Monoid Observation

    arXiv:2609.03643v1 Announce Type: cross Abstract: Let $L\subseteq\Sigma^*$ and fix a morphism $h:\Sigma^*\to M$ into a finite monoid. We study exact factorization and canonical presentation in the relative syntactic congruence $\theta_{L,h}:=\equiv_L\cap\ker h$. We separate uniqu…

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