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Strong Completeness and Limited Canonicity for PDL

2007
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Journal of Logic, Language and Information
*

Lemma 8 For every ϕ ∈ L 0 and for all

doi:10.1007/s10849-007-9051-4
fatcat:7ox3ztbsd5c3rakvuqqrbxwshm
*programs*α ∈ L 0 : ω | ϕ iff [[ϕ]] is*cofinite*(5) (ω, y) ∈ R c (α) iff {x | (x, y) ∈ [[α]]} is*cofinite*(6) (ω, ω) ∈ R c (α) iff {x | (x, x) ∈ [[α]]} is*cofinite*... Lemma 5 For every ϕ: ω | ϕ iff [[ϕ]] is*cofinite*(4) where [[ϕ]] = {x ∈ N | x | ϕ}. Proof First we show that, for every formula ϕ, [[ϕ] ] is*finite*or*cofinite*. ...##
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Complexity of Operations on Cofinite Languages
[chapter]

2010
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Lecture Notes in Computer Science
*

We study the worst case complexity of regular operations on

doi:10.1007/978-3-642-12200-2_21
fatcat:j74lq733unhtzkyeje57rbjt7a
*cofinite*languages (i.e., languages whose complement is*finite*) and provide algorithms to compute efficiently the resulting minimal automata. ... We propose two algorithms, one based on usual automata constructions and another one, easier to implement,*related*to dynamic*programming*. ... We denote automata by tuples (A, Q, T, I, F ) where Q is a*finite*set of states, A is a*finite*set of letters called alphabet, the transition*relation*T is a subset of Q × A × Q, I ⊂ Q is the set of initial ...##
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Page 2667 of Mathematical Reviews Vol. , Issue 2001D
[page]

2001
*
Mathematical Reviews
*

We characterise a class of

*programs*(via their input-output*relations*) and a class of predicates, such that each predicate is either*finite*or*cofinite*, and*programs*, when viewed as predicate transformers ... of loops with stuttering transitions.” 2001d:68147 68Q60 03B70 03G05 Brink, Chris (SA-CAPE-MAM; Rondebosch) ; Rewitzky, Ingrid (SA-CAPE-MAM; Rondebosch)*Finite*-*cofinite**program**relations*. ...##
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Engineering formal metatheory

2008
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Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '08
*

induction principles of

doi:10.1145/1328438.1328443
dblp:conf/popl/AydemirCPPW08
fatcat:fplnrrlowba4bi5zcr4fvvnguu
*relations*defined using*cofinite*quantification are strong enough for metatheoretic reasoning, and need not be explicitly strengthened. ... We propose a novel style for formalizing metatheory, combining locally nameless representation of terms and*cofinite*quantification of free variable names in inductive definitions of*relations*on terms ... We say that this definition of the typing*relation*uses "*cofinite*quantification" since we must show that the premise of C-TYPING-ABS ("C" for "*cofinite*") holds for all but*finitely*many names. ...##
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Engineering formal metatheory

2008
*
SIGPLAN notices
*

induction principles of

doi:10.1145/1328897.1328443
fatcat:g3tgwhyi4zf5rayeizyarmtawa
*relations*defined using*cofinite*quantification are strong enough for metatheoretic reasoning, and need not be explicitly strengthened. ... We propose a novel style for formalizing metatheory, combining locally nameless representation of terms and*cofinite*quantification of free variable names in inductive definitions of*relations*on terms ... We say that this definition of the typing*relation*uses "*cofinite*quantification" since we must show that the premise of C-TYPING-ABS ("C" for "*cofinite*") holds for all but*finitely*many names. ...##
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Locally Nameless Permutation Types
[article]

2017
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arXiv
*
pre-print

We show that this combination is particularly useful when formalizing

arXiv:1710.08444v1
fatcat:m7djx64c5rfafa6k5jcdts6nlq
*programming*languages where bound names may become free during execution ("extrusion"), common in process calculi. ... We explain how to use*cofinite*quantification in this setting, show why reasoning about renaming is more important here than in languages without extrusion, and provide results about infinite support, ...*Related*Work and Conclusions The treatment of names is one of the first stumbling blocks towards formalizing*programming*language theory. ...##
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RECOGNIZING STRONG RANDOM REALS

2008
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The Review of Symbolic Logic
*

For any input i, P enters a nonterminating routine that writes a nonempty,

doi:10.1017/s1755020308080076
fatcat:e5xcqqxrwrdkjofx32numbnayu
*finite*sequence b 1 , . . . , b m with b m = x i (m depends on i). 1 The*program*will not, in general, allow prediction of x ... Let real x be given, and suppose that (x[n]) = Yes for only*finitely*many n. Then, there are (*cofinitely*many) k with x ∈ [W f (k) ]. Suppose alternatively that (x[n]) = Yes for infinitely many n. ...##
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On commensurable hyperbolic Coxeter groups

2016
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Geometriae Dedicata
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For Coxeter groups acting non-cocompactly but with

doi:10.1007/s10711-016-0151-7
fatcat:mhq4rl2mi5cc7nm54mwuy4grha
*finite*covolume on real hyperbolic space H n , new methods are presented to distinguish them up to (wide) commensurability. ... This commensurability*relation*is an equivalence*relation*which preserves properties such as cocompactness,*cofiniteness*and arithmeticity. ... The commensurability*relation*is an equivalence*relation*which is stable when passing to a*finite*index subgroup. ...##
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Representations of vertex operator algebras and braided finite tensor categories
[article]

2009
*
arXiv
*
pre-print

We discuss what has been achieved in the past twenty years on the construction and study of a braided

arXiv:0903.4233v2
fatcat:szr5pafyljhp3bfuq2m7ygv6py
*finite*tensor category structure on a suitable module category for a suitable vertex operator algebra ... III V is C 2 -*cofinite*. ... The category of*finite*-dimensional modules for a*finite*group is a*finite*tensor category. ...##
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Page 1187 of Mathematical Reviews Vol. 44, Issue 6
[page]

1972
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Mathematical Reviews
*

On large cardinals and partition

*relations*. J. Symbolic Logic 36 (1971), 305-308. ... (i) For all*finite*subsets P of I*, for all*finite*subsets N of M, for all*cofinite*subsets Q’ of J, |A(P) A BQ’)| +|{A(P) UV BQ’)} 0 Nl 2|P|+|N| — Ducrans sr Oe — ier min{|J,|—¢, [{J\Q}OJ,|}, and (ii) ...##
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Abstract representation theorems for demonic refinement algebras

2010
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The Journal of Logic and Algebraic Programming
*

Acknowledgements We thank Georg Struth and the anonymous referees of this special issue of The Journal of Logic and Algebraic

doi:10.1016/j.jlap.2010.07.014
fatcat:7eprxooemngelmihp2jldzco7q
*Programming*as well as those of the 10th International Conference on*Relational*... Since the*finite*product of*finite*and/or*cofinite*subidentities is*finite*or*cofinite*(just like the*finite*intersection of*finite*and/or*cofinite*sets), it suffices to prove (;j | 0 ≤ j < n i : Gt i, ... For instance, take R to be the set of*finite*or*cofinite*subsets of the identity*relation*on the natural numbers. ...##
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The gamma construction and asymptotic invariants of line bundles over arbitrary fields
[article]

2019
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arXiv
*
pre-print

To do so over imperfect fields, we prove a scheme-theoretic version of the gamma construction of Hochster and Huneke to reduce to the setting where the ground field is F-

arXiv:1809.01217v3
fatcat:wcaeoon4wvbyvdyjm32vz5ram4
*finite*. ... Application to the minimal model*program*over imperfect fields. Let {X i } be a*finite*set of schemes essentially of*finite*type over A. ... Now let Γ ⊆ Λ be a*cofinite*subset, i.e., a subset Γ of Λ such that Λ Γ is a*finite*set. ...##
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Tensor Categories arising from the Virasoro Algebra
[article]

2021
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arXiv
*
pre-print

We show that there is a braided tensor category structure on the category of C_1-

arXiv:2002.03180v2
fatcat:f2nkm7yc4bedfncww4defdkkru
*cofinite*modules for the (universal or simple) Virasoro vertex operator algebras of arbitrary central charge. ... For example, the quantum geometric Langlands*program*can be*related*to equivalences of tensor categories of modules of W -algebras and affine vertex algebras, see [AFO, Sec. 6] for example. ... if W is. (2) If W is a*finite*-length V -module with C 1 -*cofinite*composition factors, then W is also C 1 -*cofinite*. 2.2. ...##
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On the closure of the diagonal of a T1-space

2008
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The Journal of Logic and Algebraic Programming
*

The closure of = {(x,x) : x ∈ X} in X × X is a symmetric

doi:10.1016/j.jlap.2008.02.008
fatcat:iakafymxsfgqrgujck2qhqgqjq
*relation*on X. ... We characterise those equivalence*relations*on an infinite set that arise as the closure of the diagonal with respect to a T 1 -topology. ... On an infinite set, an equivalence*relation*with*finitely*many blocks is T 1 -realisable if and only if every*finite*block is a singleton. ...##
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Mechanizing Metatheory Without Typing Contexts

2013
*
Journal of automated reasoning
*

When mechanizing the metatheory of a

doi:10.1007/s10817-013-9287-4
fatcat:mey7bsnc6zhujc3wjnici77smm
*programming*language, one usually needs many lemmas proving structural properties of typing judgments, such as permutation and weakening. ... This technique of eliminating typing contexts, which has been around since Church [4] , is based on the view that entailment*relations*, such as typing judgments, are just syntactic tools for displaying ...*Related*work Previous research on mechanizing the metatheory of*programming*languages usually focuses on the problem of representing binders to deal with α-equivalence*relations*and capture-avoiding substitutions ...
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