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The monadic theory of finite representations of infinite words
2007
Information Processing Letters
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This result can be seen as a translation, onto finite representations of infinite words, of Büchi's automata-theoretic characterization of S1S. ...
These can be seen as finite encodings of ultimately periodic words. ...
These two results can be seen as a translation, onto finite representations of infinite words, of the Büchi automata characterization theorem [3] of S1S. ...
doi:10.1016/j.ipl.2007.02.014
fatcat:nvdw46e7wzfa3b5qbllnc76vve
Recognisable Languages over Monads
[chapter]
2015
Lecture Notes in Computer Science
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This paper 1 proposes monads as a framework for algebraic language theory. Examples of monads include words and trees, finite and infinite. ...
On the abstract level of monads one can prove theorems like the Myhill-Nerode theorem, the Eilenberg theorem; one can also define profinite objects. ...
Lawvere theories can be viewed as the special case of finitary monads, e.g. finite words are Lawvere theories, but infinite words are not. ...
doi:10.1007/978-3-319-21500-6_1
fatcat:r4wqkmqoujgktdtn53bscx3mcy
Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications
[chapter]
2009
Lecture Notes in Computer Science
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This tutorial will present an overview of the use of Monadic Second-Order Logic to describe sets of finite graphs and graph transformations, in relation with the notions of tree-width and clique-width. ...
It will review applications to the construction of algorithms, to Graph Theory and to the extension to graphs of Formal Language Theory concepts. ...
Monadic second-order formulas are also used in Formal Language Theory to describe languages, i.e., sets of words or terms. ...
doi:10.1007/978-3-642-00982-2_2
fatcat:ryjvoaa7dnefrcruygfnpqso2i
Monadic Decomposability of Regular Relations
2019
International Colloquium on Automata, Languages and Programming
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Our main contribution is to fully settle the complexity of this decision problem by developing new techniques employing infinite Ramsey theory. The complexity for DFA (resp. ...
Monadic decomposibility -the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas -is a powerful tool for devising a decision ...
Acknowledgements We thank Leonid Libkin for the useful discussion. ...
doi:10.4230/lipics.icalp.2019.103
dblp:conf/icalp/BarceloHLLN19
fatcat:exrlvgpuznbsjd7mszt3d3enra
Page 4009 of Mathematical Reviews Vol. , Issue 87h
[page]
1987
Mathematical Reviews
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It shows that the monadic theory of any “context-free graph” is decidable, obtaining in this way a substan- tial extension of Rabin’s “tree theorem” (which states that the monadic theory of the binary ...
The standard theories of meaningfulness of representational propositions in these three areas are shown to be special cases of two theories of meaningfulness for arbitrary representational propositions ...
Page 513 of Mathematical Reviews Vol. , Issue 2004a
[page]
2004
Mathematical Reviews
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The usual k-automatic sequences are based on the k-adic numeration: the nth term of a sequence is produced by a deterministic finite automaton with output fed with the k-ary representation of n. ...
We show that these generate several of the
monads of primary interest that have been used to model com-
putational effects, with the striking omission of the continuations
monad. ...
Whatever Image
2003
Postmodern Culture
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This would entail thinking of the body as the locus or the generator of representation. ...
But if the body is seen as a generator of representation, what happens to art, to image, and to the broader question of representation in art criticism? ...
Every monad in Leibniz contains the entire world: the monad is finite and the world is infinite. ...
doi:10.1353/pmc.2003.0002
fatcat:zlyychrvrjcydowut2ch4qgkne
A Coalgebraic Take on Regular and omega-Regular Behaviour for Systems with Internal Moves
2018
International Conference on Concurrency Theory
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Since systems with internal moves are defined here as coalgebras for a monad, in the first part of the paper we present a construction of a monad suitable for modelling (in)finite behaviour. ...
We present a general coalgebraic setting in which we define finite and infinite behaviour with Büchi acceptance condition for systems with internal moves. ...
The finite semantics, also known as the language of finite words of Q, is defined as the set of all finite words a 1 . . . a n ∈ Σ * for which there is a sequence of transitions q 0 a1 → q 1 a2 → q 2 . ...
doi:10.4230/lipics.concur.2018.25
dblp:conf/concur/Brengos18
fatcat:2ds2smj5onhkdcvx7db43ew4ve
Monadic Decomposability of Regular Relations
[article]
2019
arXiv
pre-print
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Our main contribution is to fully settle the complexity of this decision problem by developing new techniques employing infinite Ramsey theory. The complexity for DFA (resp. ...
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision ...
The notion of "monadic decomposability" essentially captures the intuitive notion that the components in ...
arXiv:1903.00728v3
fatcat:uvgi2cxkvjeornmpbmrdxhfopq
Page 1314 of Mathematical Reviews Vol. , Issue 85d
[page]
1985
Mathematical Reviews
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The author also extends PCP to circular words, doubly infinite words and doubly infinite powers, and shows these extensions to be undecidable. ...
The modest chains are exactly the chains monadically equivalent to countable chains. The monadic theory of modest chains is decidable. ...
A coalgebraic take on regular and ω-regular behaviours
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:1902.02601v5 fatcat:bpfvrsm7xzbgnkdxky4caygkxeOther Versions
The first part of the paper is devoted to presenting a construction of a monad suitable for modelling (in)finite behaviour. ...
We present a general coalgebraic setting in which we define finite and infinite behaviour with Büchi acceptance condition for systems whose type is a monad. ...
{i | q i ∈ F} is infinite, or in other words, the run r visits the set of final states F infinitely often. ...
arXiv:1902.02601v6
fatcat:n3lads47u5c2rgdcgjneidss6q
Backward Induction for Repeated Games
2018
Electronic Proceedings in Theoretical Computer Science
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This uses the selection monad transformer, combined with the searchable set monad viewed as a notion of 'topologically compact' nondeterminism, and a simple model of computable real numbers. ...
This is the first application of Escard\'o and Oliva's theory of higher-order sequential games to games of imperfect information, in which (as well as its mathematical elegance) lazy evaluation does nontrivial ...
In particular, the monad J T R does not admit infinite products when T is the list monad, which is the most straightforward and common representation of nondeterminism in Haskell, and the one we used in ...
doi:10.4204/eptcs.275.5
fatcat:3erop35bpfghvklvwoegnefcv4
On Monadic Theories of Monadic Predicates
[chapter]
2010
Lecture Notes in Computer Science
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Prominent examples are the monadic theory of the successor structure S1 = (N, +1) of the natural numbers and the monadic theory of the binary tree, i.e., of the two-successor structure S2 = ({0, 1} * , ...
It is known that the monadic theory of (S1, P ) is decidable iff the weak monadic theory is, and that for recursive P this theory is in ∆ 0 3 , i.e. of low degree in the arithmetical hierarchy. ...
an input word α if the set of states visited infinitely often in the unique run of A on α coincides with a set in F . ...
doi:10.1007/978-3-642-15025-8_30
fatcat:giwx47rl6zaarn7u4rv5fj72pm
Composition of Path Transductions
[chapter]
2004
Lecture Notes in Computer Science
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They define strict subclasses of monadic transductions and preserve the decidability of monadic second order theory. ...
We give a generalization of the Elgot and Mezei composition theorem from rational word transductions to path transductions. ...
Our aim is to show that the relation T = T 1 · T 2 remains an unbounded path transduction. ...
doi:10.1007/978-3-540-30203-2_26
fatcat:rmak6wmv5nfnfprviv6awj7iya
Tree Automata Make Ordinal Theory Easy
[chapter]
2006
Lecture Notes in Computer Science
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We give a new simple proof of the decidability of the First Order Theory of (ω ω i , +) and the Monadic Second Order Theory of (ω i , <), improving the complexity in both cases. ...
Our algorithm is based on tree automata and a new representation of (sets of) ordinals by (infinite) trees. The present paper is partly based on [?] ...
and to the participants of Dagstuhl-Seminar "Algorithmic-Logical Theory of Infinite Structures" for interesting discussions. ...
doi:10.1007/11944836_27
fatcat:lhvcjbdb5ndyroma2moiollgfa
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