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The monadic theory of finite representations of infinite words

Anuj Dawar, David Janin
2007 Information Processing Letters  
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]

Mikołaj Bojańczyk
2015 Lecture Notes in Computer Science  
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]

Bruno Courcelle
2009 Lecture Notes in Computer Science  
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

Pablo Barceló, Chih-Duo Hong, Xuan-Bach Le, Anthony W. Lin, Reino Niskanen, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
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  
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  
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

Zafer Aracagok
2003 Postmodern Culture  
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

Tomasz Brengos, Michael Wagner
2018 International Conference on Concurrency Theory  
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]

Pablo Barcelo, Chih-Duo Hong, Xuan-Bach Le, Anthony W. Lin, Reino Niskanen
2019 arXiv   pre-print
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  
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]

Tomasz Brengos
2021 arXiv   pre-print
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

Jules Hedges
2018 Electronic Proceedings in Theoretical Computer Science  
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]

Wolfgang Thomas
2010 Lecture Notes in Computer Science  
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]

Tanguy Urvoy
2004 Lecture Notes in Computer Science  
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]

Thierry Cachat
2006 Lecture Notes in Computer Science  
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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