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A New Proof for a Strong Law of Large Numbers of Kolmogorov's Type via Weak Convergence
[article]

2020
*
arXiv
*
pre-print

Our

arXiv:2004.13501v2
fatcat:nhtqi2hhe5gc3nbzldofisw3ta
*proof*is independent of both Kolmogorov's strong law and its known*proof*(s), and potentially furnishes a*new*way to obtain a*short**proof*of Kolmogorov's strong law. ... In terms of the Dirac representation of sample mean and the weak convergence of empirical distributions that holds almost surely, we construct a*new**proof*for a strong law of large numbers of Kolmogorov's ... It would be desirable to obtain a*short**proof*of KSLLN that possibly and hopefully also gains*new*insight into the nature of the "problem". ...##
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What a Difference a Variable Makes
[chapter]

2018
*
Lecture Notes in Computer Science
*

The PR

doi:10.1007/978-3-319-89963-3_5
fatcat:jxqfz6wcyncvlixc4yry23v65q
*proof*system allows*short**proofs**without**new**variables*for some hard problems, while the DRAT*proof*system is supported by top-tier SAT solvers. ... Our simulation algorithm uses only one*new*Boolean*variable*and the size increase is at most quadratic in the size of the propositional formula and the PR*proof*. ... There are*short*PR*proofs**without**new**variables*for some hard formulas [17] . Some of them can be found automatically [18] . ...##
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Mycielski Graphs and $$\mathrm {PR}$$ Proofs
[chapter]

2020
*
Lecture Notes in Computer Science
*

In particular, we consider variants of the PR (propagation redundancy)

doi:10.1007/978-3-030-51825-7_15
fatcat:2wwnadsctnf67ehmvrkeo5nneu
*proof*system that are*without**new**variables*, and with or*without*deletion. ... These*proof*systems are of interest due to their potential uses for*proof*search. As our main result, we present a sublinear-length and constant-width PR*proof**without**new**variables*or deletion. ... For several difficult tautologies, PR has been shown to admit*proofs*that are*short*(at most polynomial length), narrow (small clause width), and*without*extension (disallowing*new**variables*) [5, 12, ...##
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Strong Extension-Free Proof Systems

2019
*
Journal of automated reasoning
*

We demonstrate the strength of our

doi:10.1007/s10817-019-09516-0
pmid:32226181
pmcid:PMC7089731
fatcat:i6es4zm4hjfx5fwyeltxtigpdi
*proof*systems on the famous pigeon hole formulas by providing*short*clausal*proofs**without**new**variables*. ... The resulting*proof*systems are surprisingly strong, even*without*the introduction of*new**variables*-a key feature of*short**proofs*presented in the*proof*-complexity literature. ... We can thus construct*short*DRAT*proofs**without**new**variables*from*short*PR*proofs**without**new**variables*. ...##
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Sorting Parity Encodings by Reusing Variables
[chapter]

2020
*
Lecture Notes in Computer Science
*

We present a technique for

doi:10.1007/978-3-030-51825-7_1
fatcat:xakudabh4fhbbcwjcwzaeczfhq
*short*clausal*proofs*that exploits these Tseitin*variables*to reorder the constraints within the DRAT system. ... Yet, implementations of these techniques either lack support of*proof*logging or introduce many extension*variables*. The compact, commonly-used encoding of parity constraints uses Tseitin*variables*. ... We show how to obtain DRAT*proofs*of size O(n log n)*without*using additional*variables*. Our method can also be used to produce ER*proofs*of similar size with*new**variables*. ...##
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DRAT and Propagation Redundancy Proofs Without New Variables
[article]

2021
*
arXiv
*
pre-print

*Without*deletion, we show that SPR^- can simulate PR^- provided only

*short*clauses are inferred by SPR inferences. ... If the

*new*clause C is allowed to include

*new*

*variables*then the systems based on these rules are all equivalent to extended resolution. ... A BC refutation of Γ

*without*

*new*

*variables*, or, for

*short*, a BC − refutation of Γ, is a BC refutation of Γ in which only

*variables*from Γ appear. ...

##
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Page 201 of The Astrophysical Journal Vol. 17, Issue 3
[page]

1903
*
The Astrophysical Journal
*

A

*NEW**VARIABLE*STAR OF UNUSUALLY*SHORT*PERIOD. By G. MULLER and P. KEMPF. ... All of our measures of the*new**variable*are summarized in tabular form below. ...##
###
A Formally Verified Calculus for Full Java Card
[chapter]

2004
*
Lecture Notes in Computer Science
*

the

doi:10.1007/978-3-540-27815-3_37
fatcat:nxq4unamavgatkbxz4ag5ez3pq
*new*heap h is bound to the*variable*H. ... [17] : "PVS can run for hours*without*completing the*proof*, or it can crash because the*proof*state becomes too big."). So work has still to be done to reduce the complexity of formal*proofs*. ... In other*proofs*only the lemmas for the findFree method are used. This allows a nice structuring of the*proofs*. ...##
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Page 6804 of Mathematical Reviews Vol. , Issue 2000j
[page]

2000
*
Mathematical Reviews
*

Givant, A formalization of set theory

*without**variables*, Amer. Math. Soc., Providence, RI, 1987; MR 89g:03012].) ... The*proof*exploits the fact that P and Q can be used to code an arbitrary m-tuple of*variables*as a single*variable*. ...##
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A new correctness criterion for MLL proof nets

2014
*
Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14
*

We propose a

doi:10.1145/2603088.2603125
dblp:conf/csl/Ehrhard14
fatcat:ew66fcgzf5bdrjowghp2a5omxa
*new*correctness criterion for constant-free Multiplicative Linear Logic with Mix which applies to a coherence space structure that a term-based*proof*structure induces on the set of its*variables*... The atomic ingredient of these terms are*variables*related by axiom links. ... Besides the fact that this "criterion" does not provide any*new*insight about*proof*nets, it is not suitable because it is difficult to prove directly -that is,*without*using another correctness criterion ...##
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Recent results on permutations without short cycles
[article]

2016
*
arXiv
*
pre-print

*New*asymptotic formulas for κ(n,r) are obtained using the saddle-point method when 5≤ r< n and n→∞. ... Recent results on permutations

*without*

*short*cycles 3 Let k j (σ) equal the number of cycles of length j in a permutation σ ∈ S n , k(σ) = (k 1 (σ), k 2 (σ), . . . , k n (σ)) , and Z = (Z 1 , Z 2 , . . ...

*New*results are the following theorems: Theorem 1 For √ n log n ≤ r < n, we have κ(n, r) = e −Hr+γ ω(n/r) + O ̺(n/r) r 2 .

*Proof*. The result is a corollary of Theorem 1 in [7] . ...

##
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The state of SAT

2007
*
Discrete Applied Mathematics
*

eliminate parts of the tree

doi:10.1016/j.dam.2006.10.004
fatcat:uouc5yqwlbhpbpd5g25ka3mdia
*without*search. ... The result was, in fact, even stronger: they showed that there are formulas with*short*clause learning*proofs*that require exponentially large regular resolution*proofs*. ...##
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Augmenting the Power of (Partial) MaxSat Resolution with Extension

2020
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

The

doi:10.1609/aaai.v34i02.5516
fatcat:yc4zw7ogyzdrnmm37cly5b42tu
*new**proof*system MaxResE is sound and complete, and more powerful than plain MaxSAT resolution, since it can refute the soft and hard PHP in polynomial time. ... In this paper we augment the MaxSAT resolution*proof*system with an extension rule. ... MaxResE with*variable*aliases can simulate the dual encoding.*Proof*. In the*proof*we allow MaxResE to add for every original*variable*x i a*new**variable*y i such that x i ↔ ¬y i . ...##
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Page 5459 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

Much space is de- voted to preservation of ancestral relations between occurrences of formulas in Gentzen-type sequent

*proofs*with and*without*cut. ... J. 37 (1997), no. 1, 46-53 Summary: “In free*variable*systems of arithmetic the problem of the replaceability of the axiom of double induction (ADI) is more interesting in the systems*without*the restricted ...##
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Proved development of the real-time properties of the IEEE 1394 Root Contention Protocol with the event-B method

2009
*
International Journal on Software Tools for Technology Transfer (STTT)
*

We present a model of the IEEE 1394 Root Contention Protocol with a

doi:10.1007/s10009-009-0130-5
fatcat:cnqfhhvw3bgh5ohst4csebztye
*proof*of Safety. ... Verification is done by*proof*using the event B method and its prover, we also have a way to model-check models. ... The whole invariant of this paper is a*proof*of that. In this refinement we have four*new**variables*: at_a_awake, at_b_awake, a_sleept, b_sleept. ...
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