相关论文: Nearly-Exponential Size Lower Bounds for Symbolic …

We revisit the satisfiability problem for two-variable logic, denoted by SAT(FO2), which is known to be NEXP-complete. The upper bound is usually derived from its well known Exponential Size Model (ESM) property. Whether it can be…

We derive an upper bound on the number of models for exact satisfiability (XSAT) of arbitrary CNF formulas F. The bound can be calculated solely from the distribution of positive and negated literals in the formula. For certain subsets of…

We analyze possibilities of second-order quantifier elimination for formulae containing parameters -- constants or functions. For this, we use a constraint resolution calculus obtained from specializing the hierarchical superposition…

Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…

We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a…

We prove a simple, nearly tight lower bound on the approximate degree of the two-level $\mathsf{AND}$-$\mathsf{OR}$ tree using symmetrization arguments. Specifically, we show that $\widetilde{\mathrm{deg}}(\mathsf{AND}_m \circ…

The minimum number of clauses in a CNF representation of the parity function $x_1 \oplus x_2 \oplus \dotsb \oplus x_n$ is $2^{n-1}$. One can obtain a more compact CNF encoding by using non-deterministic variables (also known as guess or…

We study the problem of estimating the number of defective items $d$ within a pile of $n$ elements up to a multiplicative factor of $\Delta>1$, using deterministic group testing algorithms. We bring lower and upper bounds on the number of…

This paper focuses on succinctness results for fragments of Linear Temporal Logic with Past (LTL) devoid of binary temporal operators like until, and provides methods to establish them. We prove that there is a family of cosafety languages…

We are considering RAMs $N_{n}$, with wordlength $n=2^{d}$, whose arithmetic instructions are the arithmetic operations multiplication and addition modulo $2^{n}$, the unary function $ \min\lbrace 2^{x}, 2^{n}-1\rbrace$, the binary…

We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…

The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment to contexts involving relations of arity greater than two. Quantifiers in this logic are used in…

The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are…

We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…

We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…

In this work, we consider the satisfiability problem in a logic that combines word equations over string variables denoting words of unbounded lengths, regular languages to which words belong and Presburger constraints on the length of…

We show unconditional parameterized lower bounds in the area of knowledge compilation, more specifically on the size of circuits in decomposable negation normal form (DNNF) that encode CNF-formulas restricted by several graph width…

We give strengthened provable guarantees on the performance of widely employed and empirically successful {\sl top-down decision tree learning heuristics}. While prior works have focused on the realizable setting, we consider the more…

For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…

We answer Question~3.2 from Shelah \cite{Sh:666}: Given a maximal almost disjoint (mad) family $\mathcal A$ of size $\aleph_1$, we construct a forcing ${\mathbb Q}(\mathcal A)$ that has Axiom A, is ${}^\omega \omega$-bounding, preserves…