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The monadic theory of finite representations of infinite words

2007
*
Information Processing Letters
*

This result can be seen as a translation, onto

doi:10.1016/j.ipl.2007.02.014
fatcat:nvdw46e7wzfa3b5qbllnc76vve
*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. ...##
###
Recognisable Languages over Monads
[chapter]

2015
*
Lecture Notes in Computer Science
*

This paper 1 proposes

doi:10.1007/978-3-319-21500-6_1
fatcat:r4wqkmqoujgktdtn53bscx3mcy
*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. ...##
###
Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications
[chapter]

2009
*
Lecture Notes in Computer Science
*

This tutorial will present an overview

doi:10.1007/978-3-642-00982-2_2
fatcat:ryjvoaa7dnefrcruygfnpqso2i
*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. ...##
###
Monadic Decomposability of Regular Relations

2019
*
International Colloquium on Automata, Languages and Programming
*

Our main contribution is to fully settle

doi:10.4230/lipics.icalp.2019.103
dblp:conf/icalp/BarceloHLLN19
fatcat:exrlvgpuznbsjd7mszt3d3enra
*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. ...##
###
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

2003
*
Postmodern Culture
*

This would entail thinking

doi:10.1353/pmc.2003.0002
fatcat:zlyychrvrjcydowut2ch4qgkne
*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*. ...##
###
A Coalgebraic Take on Regular and omega-Regular Behaviour for Systems with Internal Moves

2018
*
International Conference on Concurrency Theory
*

Since systems with internal moves are defined here as coalgebras for a

doi:10.4230/lipics.concur.2018.25
dblp:conf/concur/Brengos18
fatcat:2ds2smj5onhkdcvx7db43ew4ve
*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 . ...##
###
Monadic Decomposability of Regular Relations
[article]

2019
*
arXiv
*
pre-print

Our main contribution is to fully settle

arXiv:1903.00728v3
fatcat:uvgi2cxkvjeornmpbmrdxhfopq
*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 ...##
###
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]

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. ...

##
###
Backward Induction for Repeated Games

2018
*
Electronic Proceedings in Theoretical Computer Science
*

This uses

doi:10.4204/eptcs.275.5
fatcat:3erop35bpfghvklvwoegnefcv4
*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 ...##
###
On Monadic Theories of Monadic Predicates
[chapter]

2010
*
Lecture Notes in Computer Science
*

Prominent examples are

doi:10.1007/978-3-642-15025-8_30
fatcat:giwx47rl6zaarn7u4rv5fj72pm
*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 . ...##
###
Composition of Path Transductions
[chapter]

2004
*
Lecture Notes in Computer Science
*

They define strict subclasses

doi:10.1007/978-3-540-30203-2_26
fatcat:rmak6wmv5nfnfprviv6awj7iya
*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. ...##
###
Tree Automata Make Ordinal Theory Easy
[chapter]

2006
*
Lecture Notes in Computer Science
*

We give a new simple proof

doi:10.1007/11944836_27
fatcat:lhvcjbdb5ndyroma2moiollgfa
*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. ...
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