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Strong Completeness and Limited Canonicity for PDL
2007
Journal of Logic, Language and Information
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Lemma 8 For every ϕ ∈ L 0 and for all 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. ...
doi:10.1007/s10849-007-9051-4
fatcat:7ox3ztbsd5c3rakvuqqrbxwshm
Complexity of Operations on Cofinite Languages
[chapter]
2010
Lecture Notes in Computer Science
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We study the worst case complexity of regular operations on 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 ...
doi:10.1007/978-3-642-12200-2_21
fatcat:j74lq733unhtzkyeje57rbjt7a
Page 2667 of Mathematical Reviews Vol. , Issue 2001D
[page]
2001
Mathematical Reviews
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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. ...
Engineering formal metatheory
2008
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '08
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induction principles of 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. ...
doi:10.1145/1328438.1328443
dblp:conf/popl/AydemirCPPW08
fatcat:fplnrrlowba4bi5zcr4fvvnguu
Engineering formal metatheory
2008
SIGPLAN notices
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induction principles of 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. ...
doi:10.1145/1328897.1328443
fatcat:g3tgwhyi4zf5rayeizyarmtawa
Locally Nameless Permutation Types
[article]
2017
arXiv
pre-print
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We show that this combination is particularly useful when formalizing 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. ...
arXiv:1710.08444v1
fatcat:m7djx64c5rfafa6k5jcdts6nlq
RECOGNIZING STRONG RANDOM REALS
2008
The Review of Symbolic Logic
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For any input i, P enters a nonterminating routine that writes a nonempty, 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. ...
doi:10.1017/s1755020308080076
fatcat:e5xcqqxrwrdkjofx32numbnayu
On commensurable hyperbolic Coxeter groups
2016
Geometriae Dedicata
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For Coxeter groups acting non-cocompactly but with 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. ...
doi:10.1007/s10711-016-0151-7
fatcat:mhq4rl2mi5cc7nm54mwuy4grha
Representations of vertex operator algebras and braided finite tensor categories
[article]
2009
arXiv
pre-print
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We discuss what has been achieved in the past twenty years on the construction and study of a braided 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. ...
arXiv:0903.4233v2
fatcat:szr5pafyljhp3bfuq2m7ygv6py
Page 1187 of Mathematical Reviews Vol. 44, Issue 6
[page]
1972
Mathematical Reviews
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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) ...
Abstract representation theorems for demonic refinement algebras
2010
The Journal of Logic and Algebraic Programming
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Acknowledgements We thank Georg Struth and the anonymous referees of this special issue of The Journal of Logic and Algebraic 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. ...
doi:10.1016/j.jlap.2010.07.014
fatcat:7eprxooemngelmihp2jldzco7q
The gamma construction and asymptotic invariants of line bundles over arbitrary fields
[article]
2019
arXiv
pre-print
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2018 pre-print arXiv:1809.01217v2 fatcat:wraq4t6qlvdttiy7kj747tuxhqOther Versions
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-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. ...
arXiv:1809.01217v3
fatcat:wcaeoon4wvbyvdyjm32vz5ram4
Tensor Categories arising from the Virasoro Algebra
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2002.03180v1 fatcat:2hfrrmycwbc6jb6gyl3jd5boma
We show that there is a braided tensor category structure on the category of C_1-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. ...
arXiv:2002.03180v2
fatcat:f2nkm7yc4bedfncww4defdkkru
On the closure of the diagonal of a T1-space
2008
The Journal of Logic and Algebraic Programming
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The closure of = {(x,x) : x ∈ X} in X × X is a symmetric 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. ...
doi:10.1016/j.jlap.2008.02.008
fatcat:iakafymxsfgqrgujck2qhqgqjq
Mechanizing Metatheory Without Typing Contexts
2013
Journal of automated reasoning
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When mechanizing the metatheory of a 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 ...
doi:10.1007/s10817-013-9287-4
fatcat:mey7bsnc6zhujc3wjnici77smm
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