Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313484416> ?p ?o ?g. }
Showing items 1 to 49 of
49
with 100 items per page.
- W4313484416 abstract "This paper explains how any nondeterministic automaton for a regular language $L$ gives rise to a one-dimensional oriented Topological Quantum Field Theory (TQFT) with inner endpoints and zero-dimensional defects labelled by letters of the alphabet for $L$. The TQFT is defined over the Boolean semiring $mathbb{B}$. Different automata for a fixed language $L$ produce TQFTs that differ by their values on decorated circles, while the values on decorated intervals are described by the language $L$. The language $L$ and the TQFT associated to an automaton can be given a path integral interpretation. In this TQFT the state space of a one-point 0-manifold is a free module over $mathbb{B}$ with the basis of states of the automaton. Replacing a free module by a finite projective $mathbb{B}$-module $P$ allows to generalize automata and this type of TQFT to a structure where defects act on open subsets of a finite topological space. Intersection of open subsets induces a multiplication on $P$ allowing to extend the TQFT to a TQFT for one-dimensional foams (oriented graphs with defects modulo a suitable equivalence relation). A linear version of these constructions is also explained, with the Boolean semiring replaced by a commutative ring." @default.
- W4313484416 created "2023-01-06" @default.
- W4313484416 creator A5003562007 @default.
- W4313484416 creator A5047610019 @default.
- W4313484416 creator A5052377308 @default.
- W4313484416 creator A5064859862 @default.
- W4313484416 creator A5081122735 @default.
- W4313484416 date "2023-01-02" @default.
- W4313484416 modified "2023-09-27" @default.
- W4313484416 title "Automata and one-dimensional TQFTs with defects" @default.
- W4313484416 doi "https://doi.org/10.48550/arxiv.2301.00700" @default.
- W4313484416 hasPublicationYear "2023" @default.
- W4313484416 type Work @default.
- W4313484416 citedByCount "0" @default.
- W4313484416 crossrefType "posted-content" @default.
- W4313484416 hasAuthorship W4313484416A5003562007 @default.
- W4313484416 hasAuthorship W4313484416A5047610019 @default.
- W4313484416 hasAuthorship W4313484416A5052377308 @default.
- W4313484416 hasAuthorship W4313484416A5064859862 @default.
- W4313484416 hasAuthorship W4313484416A5081122735 @default.
- W4313484416 hasBestOaLocation W43134844161 @default.
- W4313484416 hasConcept C114614502 @default.
- W4313484416 hasConcept C118615104 @default.
- W4313484416 hasConcept C202444582 @default.
- W4313484416 hasConcept C21696900 @default.
- W4313484416 hasConcept C33923547 @default.
- W4313484416 hasConcept C7503960 @default.
- W4313484416 hasConceptScore W4313484416C114614502 @default.
- W4313484416 hasConceptScore W4313484416C118615104 @default.
- W4313484416 hasConceptScore W4313484416C202444582 @default.
- W4313484416 hasConceptScore W4313484416C21696900 @default.
- W4313484416 hasConceptScore W4313484416C33923547 @default.
- W4313484416 hasConceptScore W4313484416C7503960 @default.
- W4313484416 hasLocation W43134844161 @default.
- W4313484416 hasOpenAccess W4313484416 @default.
- W4313484416 hasPrimaryLocation W43134844161 @default.
- W4313484416 hasRelatedWork W1978042415 @default.
- W4313484416 hasRelatedWork W1989920940 @default.
- W4313484416 hasRelatedWork W2017331178 @default.
- W4313484416 hasRelatedWork W2139006188 @default.
- W4313484416 hasRelatedWork W2260035625 @default.
- W4313484416 hasRelatedWork W2523674504 @default.
- W4313484416 hasRelatedWork W2976797620 @default.
- W4313484416 hasRelatedWork W3086542228 @default.
- W4313484416 hasRelatedWork W3178663470 @default.
- W4313484416 hasRelatedWork W4249580765 @default.
- W4313484416 isParatext "false" @default.
- W4313484416 isRetracted "false" @default.
- W4313484416 workType "article" @default.