Related papers: A Generalized Resolution Proof Schema and the Pige…
We show exponential lower bounds on resolution proof length for pigeonhole principle (PHP) formulas and perfect matching formulas over highly unbalanced, sparse expander graphs, thus answering the challenge to establish strong lower bounds…
Cut-elimination theorems constitute one of the most important classes of theorems of proof theory. Since Gentzen's proof of the cut-elimination theorem for the system $\mathbf{LK}$, several other proofs have been proposed. Even though the…
Let \Omega be a set of unsatisfiable clauses, an implicit resolution refutation of \Omega is a circuit \beta with a resolution proof {\alpha} of the statement "\beta describes a correct tree-like resolution refutation of \Omega". We show…
We study the complexity of computational problems arising from existence theorems in extremal combinatorics. For some of these problems, a solution is guaranteed to exist based on an iterated application of the Pigeonhole Principle. This…
The block-iterative projections (BIP) method of Aharoni and Censor [Block-iterative projection methods for parallel computation of solutions to convex feasibility problems, Linear Algebra and its Applications 120, (1989), 165--175] is an…
The Permutation Equivalence Problem (PEP) for linear codes is a fundamental problem in coding theory and cryptography. A recent reduction shows that PEP for Linear Complementary Dual (LCD) codes reduces to Graph Isomorphism (GI) via…
Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its…
In the last twenty years, several approaches to higher-order rewriting have been proposed, among which Klop's Combinatory Rewrite Systems (CRSs), Nipkow's Higher-order Rewrite Systems (HRSs) and Jouannaud and Okada's higher-order algebraic…
We describe a method of model checking called Computing Range Reduction (CRR). The CRR method is based on derivation of clauses that reduce the set of traces of reachable states in such a way that at least one counterexample remains (if…
We formalize various counting principles and compare their strengths over $V^{0}$. In particular, we conjecture the following mutual independence between: (1) a uniform version of modular counting principles and the pigeonhole principle for…
We generalize two-point interpolatory Hermite quadrature to functions with available values and the first (n-1) derivatives at both end points. Armed with integration by parts in the reverse form we provide an elementary derivation of an…
Merge Resolution (MRes [Beyersdorff et al. J. Autom. Reason.'2021]) is a recently introduced proof system for false QBFs. It stores the countermodels as merge maps. Merge maps are deterministic branching programs in which isomorphism…
To find consistent initial data points for a system of differential-algebraic equations, requires the identification of its missing constraints. An efficient class of structural methods exploiting a dependency graph for this task was…
In this paper we propose a new statistical stopping rule for constrained maximum likelihood iterative algorithms applied to ill-posed inverse problems. To this aim we extend the definition of Tikhonov regularization in a statistical…
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…
We present a new method for computing core universal solutions in data exchange settings specified by source-to-target dependencies, by means of SQL queries. Unlike previously known algorithms, which are recursive in nature, our method can…
Counterfactual explanations (CEs) provide an intuitive way to understand recommender systems by identifying minimal modifications to user-item interactions that alter recommendation outcomes. Existing CE methods for recommender systems,…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
Sequential recommender systems have become increasingly important in real-world applications that model user behavior sequences to predict their preferences. However, existing sequential recommendation methods predominantly rely on…
This paper redefines the foundations of asymmetric cryptography's homomorphic cryptosystems through the application of the Yoneda Lemma. It demonstrates that widely adopted systems, including ElGamal, RSA, Benaloh, Regev's LWE, and…