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

Yu-Lin Chou
2020 arXiv   pre-print
Our 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".  ... 
arXiv:2004.13501v2 fatcat:nhtqi2hhe5gc3nbzldofisw3ta

What a Difference a Variable Makes [chapter]

Marijn J. H. Heule, Armin Biere
2018 Lecture Notes in Computer Science  
The PR 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] .  ... 
doi:10.1007/978-3-319-89963-3_5 fatcat:jxqfz6wcyncvlixc4yry23v65q

Mycielski Graphs and $$\mathrm {PR}$$ Proofs [chapter]

Emre Yolcu, Xinyu Wu, Marijn J. H. Heule
2020 Lecture Notes in Computer Science  
In particular, we consider variants of the PR (propagation redundancy) 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,  ... 
doi:10.1007/978-3-030-51825-7_15 fatcat:2wwnadsctnf67ehmvrkeo5nneu

Strong Extension-Free Proof Systems

Marijn J. H. Heule, Benjamin Kiesl, Armin Biere
2019 Journal of automated reasoning  
We demonstrate the strength of our 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.  ... 
doi:10.1007/s10817-019-09516-0 pmid:32226181 pmcid:PMC7089731 fatcat:i6es4zm4hjfx5fwyeltxtigpdi

Sorting Parity Encodings by Reusing Variables [chapter]

Leroy Chew, Marijn J. H. Heule
2020 Lecture Notes in Computer Science  
We present a technique for 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.  ... 
doi:10.1007/978-3-030-51825-7_1 fatcat:xakudabh4fhbbcwjcwzaeczfhq

DRAT and Propagation Redundancy Proofs Without New Variables [article]

Sam Buss, Neil Thapen
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.  ... 
arXiv:1909.00520v6 fatcat:4qubgnlak5eyfbmtdt2agnmqi4

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]

Kurt Stenzel
2004 Lecture Notes in Computer Science  
the 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.  ... 
doi:10.1007/978-3-540-27815-3_37 fatcat:nxq4unamavgatkbxz4ag5ez3pq

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.  ... 

A new correctness criterion for MLL proof nets

Thomas Ehrhard
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 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  ... 
doi:10.1145/2603088.2603125 dblp:conf/csl/Ehrhard14 fatcat:ew66fcgzf5bdrjowghp2a5omxa

Recent results on permutations without short cycles [article]

Robertas Petuchovas
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] .  ... 
arXiv:1605.02690v1 fatcat:qeup2d5oqbczbp3clnyity72gm

The state of SAT

Henry Kautz, Bart Selman
2007 Discrete Applied Mathematics  
eliminate parts of the tree 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.  ... 
doi:10.1016/j.dam.2006.10.004 fatcat:uouc5yqwlbhpbpd5g25ka3mdia

Augmenting the Power of (Partial) MaxSat Resolution with Extension

Javier Larrosa, Emma Rollon
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
The 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 .  ... 
doi:10.1609/aaai.v34i02.5516 fatcat:yc4zw7ogyzdrnmm37cly5b42tu

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  ... 

Proved development of the real-time properties of the IEEE 1394 Root Contention Protocol with the event-B method

Joris Rehm
2009 International Journal on Software Tools for Technology Transfer (STTT)  
We present a model of the IEEE 1394 Root Contention Protocol with a 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.  ... 
doi:10.1007/s10009-009-0130-5 fatcat:cnqfhhvw3bgh5ohst4csebztye
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