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Syntactic Monoids in a Category
[article]
2015
arXiv
pre-print
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The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. ...
This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids of Rabin and Scott (D = sets), the syntactic semirings of Polak (D ...
In other words, V L is the smallest local variety containing L rev .
1 Jiří Adámek, Stefan Milius, , and Henning Urbat. Syntactic monoids in a category. ...
arXiv:1504.02694v2
fatcat:2cgebp2atzhh7jg367iqdkuk3e
Syntactic Monoids in a Category
2015
Conference on Algebra and Coalgebra in Computer Science
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The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. ...
This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids of Rabin and Scott (D " sets), the syntactic semirings of Polák (D ...
In the present paper we take a more general and conceptual approach by studying algebraic recognition in a symmetric monoidal closed category D. ...
doi:10.4230/lipics.calco.2015.1
dblp:conf/calco/AdamekMU15
fatcat:cvyl4vu5qnhmnfqrh3upjfxto4
A Categorical Approach to Syntactic Monoids
[article]
2018
arXiv
pre-print
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The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. ...
This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids of Rabin and Scott ( D= sets), the syntactic ordered monoids of Pin ...
In Corollary 3.10 we give a natural condition on a monoidal category that ensures the existence of a syntactic D-monoid for every language L. ...
arXiv:1804.03011v1
fatcat:bdoqbm2lcraybecltxv65mnafe
Regular Monoidal Languages
[article]
2022
arXiv
pre-print
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We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. ...
We use the algebra of monoidal and cartesian restriction categories to investigate the properties of regular monoidal languages, and provide sufficient conditions for their recognizability by deterministic ...
The syntactic pro of a monoidal language In this section we introduce the syntactic congruence on monoidal languages and the corresponding syntactic pro, by analogy with the syntactic congruence on classical ...
arXiv:2207.00526v1
fatcat:l4mft7qrsjhypjiv4g2cmxjad4
A Topological Approach to Recognition
[chapter]
2010
Lecture Notes in Computer Science
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For regular languages, one recovers the notions of a syntactic monoid and of a free profinite monoid. For nonregular languages, the syntactic space is no longer a monoid but is still a compact space. ...
, this completion, called the syntactic space of the BA, is a compact monoid if and only if all the languages of the BA are regular. ...
In the case of a monoid, this amounts to working in the category of semiuniform monoids and imposes closure under quotients of the Boolean algebra. ...
doi:10.1007/978-3-642-14162-1_13
fatcat:o5vlbykiszbkxcsxaqjsmnr5sq
Quantaloidal nuclei, the syntactic congruence and tree automata
1992
Journal of Pure and Applied Algebra
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In the tree automata case, one really is interested in the syntactic category or syntactic quantaloid, not in monoids. ...
is enriched in the symmetric, monoidal, closed category 99 of sup-lattices. Note that the horn-sets 2(u, a) are unital quantales for all a E 9%. ...
doi:10.1016/0022-4049(92)90085-t
fatcat:2j4lxdpujzbpphue44mw24bl4m
Complexity of Grammar Induction for Quantum Types
2014
Electronic Proceedings in Theoretical Computer Science
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Most categorical models of meaning use a functor from the syntactic category to the semantic category. ...
valid reduction at the syntactic level. ...
Special thanks go to Jamie Vicary who helped me a lot by supervising and reviewing my work. ...
doi:10.4204/eptcs.172.16
fatcat:gu6fzvndrzgs7flxtzhmtwst5m
Observational Equivalence for Synchronized Graph Rewriting with Mobility
[chapter]
2001
Lecture Notes in Computer Science
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We use the framework of synchronized graph rewriting with mobility which we describe in two different, but operationally equivalent ways: on graphs defined as syntactic judgements and by using tile logic ...
Furthermore we introduce an up-to technique simplifying bisimilarity proofs and use it in an example to show the equivalence of a communication network and its specification. ...
A gs-monoidal category G is a sixtuple (C, ⊗, e, ρ, ∇, !) where (C, ⊗, e, ρ) is a symmetric strict monoidal category and ! ...
doi:10.1007/3-540-45500-0_7
fatcat:miux6zxvljgeljhdodmjaw7lgy
Syntactic Semigroups
[chapter]
1997
Handbook of Formal Languages
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Acknowledgements I would like to thank Jorge Almeida, Mario Branco and Pascal Weil for many useful suggestions on a rst version of this chapter. ...
and a 2 A, (4) idempotents commute in the syntactic monoid of K. ...
Categories Some algebraic developments in semigroup theory motivate the introduction of categories as a generalization of monoids. ...
doi:10.1007/978-3-642-59136-5_10
fatcat:yvcpa66flrc6pgfpw5l27yma5q
Syntactic Structures of Regular Languages
[article]
2017
arXiv
pre-print
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We introduce here the notion of syntactic lattice algebra which is an analogy of the syntactic monoid and of the syntactic semiring. We present a unified approach to get those three structures. ...
same way as in the category of sets Set. ...
Not every finite monoid is isomorphic to a syntactic one, we have to generate the appropriate pseudovariety. Similarly in remaining levels. Monoids. ...
arXiv:1612.06247v2
fatcat:s5syxkpcezgk3msqzkwcf6psty
Second-Order and Dependently-Sorted Abstract Syntax
2008
Logic in Computer Science
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As a matter of illustration, a model is used to extract a second-order syntactic theory, which is thus guaranteed to be correct by construction. ...
The paper develops a mathematical theory in the spirit of categorical algebra that provides a model theory for second-order and dependently-sorted syntax. ...
Definition 1 . 1 Let (C , I, ⊗) be a monoidal category. ...
doi:10.1109/lics.2008.38
dblp:conf/lics/Fiore08
fatcat:escklbzumnckpcdhcvqjedqu24
Rewriting in Free Hypergraph Categories
2017
Electronic Proceedings in Theoretical Computer Science
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We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. ...
In this work we give a combinatorial characterisation of arrows of a free hypergraph category as cospans of labelled hypergraphs and establish a precise correspondence between rewriting modulo Frobenius ...
We sometimes write a f − → b or b f ← − a for f : a → b , or also f − → and f ← − if object names are immaterial for the context. We write ⊕ for the monoidal product in a monoidal category. ...
doi:10.4204/eptcs.263.2
fatcat:meiolnyhvfhafci7ymy65jjmle
Semigroups and languages of dot-depth two
1988
Theoretical Computer Science
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The condition is formulated in terms of a novel use of categories in semigroup theory, recently developed by Tilson. ...
I conjecture an effective criterion, based on the syntactic monoid of the language, for determining whether a given language has dot-depth two, and prove the conjecture in the case of languages over an ...
Acknowledgment I am grateful to John Rhodes and Bret Tilson for sharing with me their work on categories and block products while it was still in its formative stage, and to Stuart Margolis, Jean-Eric ...
doi:10.1016/0304-3975(88)90034-5
fatcat:22qveyh25naz5a3iz2wtxeq66m
Page 8668 of Mathematical Reviews Vol. , Issue 2004k
[page]
2004
Mathematical Reviews
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In addition, the following examples are given: (1) a 2-permutational language that has a commutative infinite syntactic monoid, (2) a 3-permutational language with a non-permutational syntactic monoid. ...
It is well-known that a language L is recognized by a finite state automaton if and only if its syntactic monoid is finite. In this case such a language L is called regular. ...
On Pseudovarieties of Semiring Homomorphisms
[chapter]
2004
Lecture Notes in Computer Science
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An idempotent semiring is a structure (S, ·, ∨) where (S, ·) is a monoid with the neutral element 1, (S, ∨) is a semilattice with the smallest element 0, Syntactic structures An idempotent semiring is ...
Syntactic structures An idempotent semiring is a structure (S, ·, ∨) where (S, ·) is a monoid with the neutral element 1, (S, ∨) is a semilattice with the smallest element 0, ( ∀ a, b, c ∈ S )( a(b ∨ c ...
syntactic monoid. ...
doi:10.1007/978-3-540-28629-5_49
fatcat:6m2aqx3ivjen3p63ikt4wsyfoa
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