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The monadic second-order logic of graphs IX: Machines and their behaviours

1995
*
Theoretical Computer Science
*

We establish that every

doi:10.1016/0304-3975(95)00049-3
fatcat:wsafzocuc5dbjps5vuoywdl7kq
*monadic**second*-*order*property*of**the*behauiour*of*a*machine*(transition systems*and*tree automata are typical examples*of**machines*) is a*monadic*secondorder property*of**the**machine*... In this way, we clarify*the*distinction between "dynamic" properties*of**machines*(i.e., properties*of**their**behaviours*),*and**their*"static" properties (i.e., properties*of**the**graphs*or relational structures ... Makowsky*and*D. Niwinski for helpful comments on first versions*of*this paper. ...##
###
The monadic second-order logic of graphs V: on closing the gap between definability and recognizability

1991
*
Theoretical Computer Science
*

.,

doi:10.1016/0304-3975(91)90387-h
fatcat:tcmkji73gbbi7npb2fdh77gusm
*The**monadic**second*-*order**logic**of**graphs*V: on closing*the*gap between definability*and*recognizability, Theoretical Computer Science 80 (1991) 153-202. ... A subset*of**the*set*of**graphs*generated by such a grammar is recognizable iff it is definable in*monadic**second*-*order**logic*, whereas, in general, only*the*"'if" direction holds. * This work has been ~upponed ... Some preliminary remarks*and*notations are necessary. Let t c RM(P),,. Then G = rh~(t):= K(t)/~ ~ FG(A). where K(t)*and*~ are as in Definition 4.5. We shall use*the*notation*of*this definition. ...##
###
Master index volumes 151–160

1996
*
Theoretical Computer Science
*

Astesiano
152 (1) (1995) 91-138
154 (1) (1996) 57765
Courcelle, B.,

doi:10.1016/s0304-3975(96)90073-0
fatcat:tce2dpuyzne4de6ygz7er7tzjq
*The**monadic**second*-*order**logic**of**graphs**IX*:*Machines**and**their**behaviours*151 (1) (1995) 1255162 Courcelle, B.,*The**monadic**second*-*order*...*logic**of**graphs**IX*: Linear*orderings*(Fundamental Study) 160 (I-2) (1996) 87-143 154 (1) (1996) 3322 De Boer, F.S., A. ...##
###
Parallel and Concurrent Programming in Haskell
[chapter]

2012
*
Lecture Notes in Computer Science
*

In

doi:10.1007/978-3-642-32096-5_7
fatcat:vaj62c3ijre3nof5dchrrlfv4m
*order*to take advantage*of**the*parallelism here, all we need to do is express*the**graph*in*the*Par*monad*: For each edge in*the**graph*we make an IVar (here ia, ib*and*so on). ...*The**order**of**the*fork calls is irrelevant -*the*Par*monad*will execute*the**graph*, resolving*the*dependencies at runtime. ...*The*remote framework includes some peer discovery mechanisms that are designed to automatically locate*and*connect to other instances running on*the*same*machine*or other*machines*on*the*local network. ...##
###
Page 4265 of Mathematical Reviews Vol. , Issue 86i
[page]

1986
*
Mathematical Reviews
*

Soc. 71 (1965), 767-770; MR 32 #7413;

*The**monadic**second*-*order*theory*of*w,, 1-127, Lecture Notes in Math., 328, Springer, Berlin, 1973; MR 57 #16033]. ... finite set*of*states, M C S x*Ix*S is*the*transition relation, so is*the*initial state*and*F C S is*the*set*of*accepting states. ...##
###
Reference list of indexed articles

1995
*
Theoretical Computer Science
*

Courcelle,

doi:10.1016/0304-3975(95)80003-4
fatcat:5nnk76aalje5potfoeg7hksbce
*Monadic**second*-*order*detinable*graph*transductions: a survey 126 (I) (1994) 53375 406. M. Dam. CTL**and*ECTL' as fragments*of**the*modal p-calculus 126 (1) (1994) 77 -96 407. ... Mosbah,*Monadic**second*-*order*evaluations on tree-decomposable*graphs*109 (I-2) (1993) 49982 128. F. Drewes, Recognising k-connected hypergraphs m cubtc time 109 (l--2) (1993) 83-122 129. H. ...##
###
Algebraic theories, monads, and arities
[article]

2011
*
arXiv
*
pre-print

This Master thesis compiles

arXiv:1110.3294v1
fatcat:7xhovcib7fcenaybwuekxuloam
*the*required material in*order*to understand this question*of*arities*and*reconstruction*of**monads*,*and*tries to give some examples*of*relevant interest from both semantics ... It turns out that*the*idea behind usual notion finitary*monads*(whose values on all sets can be computed from*their*values on finite sets) extends to a more general class*of**monads*called*monads*with arities ...*Their*concatenation, again, gives*the*(underlying*graph**of**the*) free category T G: all*the*required conditions on µ*and*η are satisfied,*and*(T, µ, η) is a*monad*on*Graph*. ...##
###
Relational semantics of linear logic and higher-order model-checking
[article]

2015
*
arXiv
*
pre-print

We briefly explain in

arXiv:1501.04789v3
fatcat:4yd3ryhkpzgzfhpy52fctlmglq
*the*end*of**the*paper how his analysis driven by linear*logic*results in a new*and*purely semantic proof*of*decidability*of**the*formulas*of**the**monadic**second*-*order**logic*for higher-*order*... In this article, we develop a new*and*somewhat unexpected connection between higher-*order*model-checking*and*linear*logic*. ...*The*definitions*of*HORS*and*APT, as well as*the*correspondence between APT*and**monadic**second*-*order**logic*, are recalled in*the*Appendix. ...##
###
Parameterised notions of computation

2009
*
Journal of functional programming
*

Examples

doi:10.1017/s095679680900728x
fatcat:nmc5pit72bfqhdre2bla4it4pu
*of*such are composable continuations, side-effects where*the*type*of**the*state varies*and*input/output where*the*range*of*inputs*and*outputs varies. ... We present generalisations*of*both computational*monads**and*Freyd categories, which we call parameterised*monads**and*parameterised Freyd categories, that also capture computational effects with parameters ... As an application*of*this construction, consider*the*category StkPrg*of*simple stack*machine*programs, which is*the*free category on*the**graph*whose objects are natural numbers denoting stack depths*and*...##
###
Deductive verification of simple foraging robotic behaviours

2009
*
International Journal of Intelligent Computing and Cybernetics
*

Purpose -

doi:10.1108/17563780911005818
fatcat:lkbp34ar7vdc7onmtitjiww244
*The*purpose*of*this paper is to consider*the**logical*specification,*and*automated verification,*of*high-level robotic*behaviours*. ... This leads towards*the*use*of*first-*order*temporal*logics*(FOTLs). Findings -*The*proofs*of*many properties are achieved using automatic deductive temporal provers for*the*propositional*and*FOTLs. ... Abdelkader Behdenna was partially supported by*the*Department*of*Computer Science at*the*University*of*Liverpool. ...##
###
Computational Complexity of Deciding Provability in Linear Logic and its Fragments
[article]

2021
*
arXiv
*
pre-print

Linear

arXiv:2110.00562v1
fatcat:a6sidawnbjh5jpf2cvrermfrcy
*logic*was conceived in 1987 by Girard*and*, in contrast to classical*logic*, restricts*the*usage*of**the*structural inference rules*of*weakening*and*contraction. ... We prove an original complexity characterization*of*a fragment*of**the**logic**and*present ideas for a new, structural approach to*the*examination*of*provability in linear*logic*. ... Intuitionistic Linear*Logic*ILL undecidable [ ] First-*Order*Linear*Logic*LL 1 undecidable [ ] First-*Order*MALL MALL 1 NEXP-complete [ ] First-*Order*MLL MLL 1 NP-complete [ ]*Second*-*Order*...##
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State in Haskell

1995
*
LISP and Symbolic Computation
*

Some algorithms make critical internal use

doi:10.1007/bf01018827
fatcat:6hwpssbd7ra6vnzjmx6twvwghe
*of*updatable state, even though*their*external speci cation is purely functional. ... type MutVar s a is*the*type*of*references allocated from a state indexed by s,*and*containing a value*of*type a. ...*of*evaluation*order*. ...##
###
Logical Relations and Parametricity – A Reynolds Programme for Category Theory and Programming Languages

2014
*
Electronical Notes in Theoretical Computer Science
*

John Reynolds's pioneering work on

doi:10.1016/j.entcs.2014.02.008
fatcat:g5pch3ow6jdo7c7k5dxx4q6zw4
*logical*relations*and*relational parametricity [42] (with support from*the*earlier insights*of*Christopher Strachey, Dana Scott*and*Gordon Plotkin) casts doubt on this ...*logical*relations in*the*broader mathematical thought. ... Since*their**logical*relations subsume*the*morphisms via*the**graph*construction − ,*the*preservation*of**logical*relations automatically implies*the*preservation*of*morphisms as well. ...##
###
A predicate transformer semantics for effects (functional pearl)

2019
*
Proceedings of the ACM on Programming Languages (PACMPL)
*

This paper presents a predicate transformer semantics for a variety

doi:10.1145/3341707
fatcat:n4xh4s3yarfpdc63tvog3zzpja
*of*effects, including exceptions, state, non-determinism,*and*general recursion. ... Reasoning about programs that use effects can be much harder than reasoning about*their*pure counterparts. ... ACKNOWLEDGMENTS We would like to thank*the*members*of*Utrecht University's Software Technology Reading Group*and**the*members*of*IFIP WG 2.1 for feedback on this work. ...##
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A Büchi-Elgot-Trakhtenbrot theorem for automata with MSO graph storage

2019
*
Discrete Mathematics & Theoretical Computer Science
*

For each MSO

doi:10.23638/dmtcs-22-4-3
fatcat:6rqd6xf4efbl7g5h6kk7pshptm
*graph*storage type, we define an MSO*logic*which is a subset*of**the*usual MSO*logic*on*graphs*. We prove a B\"uchi-Elgot-Trakhtenbrot theorem, both for*the*string case*and**the**graph*case. ... An MSO*graph*storage type has MSO-definable sets*of**graphs*as storage configurations*and*as storage transformations. ... Acknowledgements We wish to thank Helmut Seidl for pointing out*the*relationship to automatic structures. We are grateful to*the*reviewers for*their*constructive comments. ...
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