Related papers: Two Lower Bounds for BPA
The problem of minimizing a polynomial over the standard simplex is one of the basic NP-hard nonlinear optimization problems --- it contains the maximum clique problem in graphs as a special case. It is known that the problem allows a…
We present a strongly exponential lower bound that applies both to the subset synchronization threshold for binary deterministic automata and to the careful synchronization threshold for binary partial automata. In the later form, the…
This paper proposes near-optimal algorithms for the pure-exploration linear bandit problem in the fixed confidence and fixed budget settings. Leveraging ideas from the theory of suprema of empirical processes, we provide an algorithm whose…
We present an efficient reduction from the Bounded integer programming (BIP) to the Subspace avoiding problem (SAP) in lattice theory. The reduction has some special properties with some interesting consequences. The first is the new upper…
We study the complexity of multiplication in noncommutative group algebras which is closely related to the complexity of matrix multiplication. We characterize such semisimple group algebras of the minimal bilinear complexity and show…
We present $\textbf{P}$robabilistically $\textbf{T}$ightened $\textbf{Li}$near $\textbf{R}$elaxation-based $\textbf{P}$erturbation $\textbf{A}$nalysis ($\texttt{PT-LiRPA}$), a novel framework that combines over-approximation techniques from…
We derive novel conditions that guarantee convergence of the Sum-Product algorithm (also known as Loopy Belief Propagation or simply Belief Propagation) to a unique fixed point, irrespective of the initial messages. The computational…
Timed basic parallel processes (TBPP) extend communication-free Petri nets (aka. BPP or commutative context-free grammars) by a global notion of time. TBPP can be seen as an extension of timed automata (TA) with context-free branching…
The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…
We show that the conditional independence (CI) implication problem with bounded cardinalities, which asks whether a given CI implication holds for all discrete random variables with given cardinalities, is co-NEXPTIME-hard. The problem…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…
Gibbons and Korach studied a fundamental problem in 1997: given an observed sequence of reads and writes of a multi-threaded program, does there exist an interleaving which is sequentially consistent? Apart from applications in testing…
This note is a commentary on, and critique of, Andre Luiz Barbosa's paper entitled "P != NP Proof." Despite its provocative title, what the paper is seeking to do is not to prove P \neq NP in the standard sense in which that notation is…
We prove that if the linear-time and polynomial-time hierarchies coincide, then every model of $\Pi_1(\mathbb{N}) + \neg \Omega_1$ has a proper end-extension to a model of $\Pi_1(\mathbb{N})$, and so $\Pi_1(\mathbb{N}) + \neg \Omega_1…
LTL synthesis -- the construction of a function to satisfy a logical specification formulated in Linear Temporal Logic -- is a 2EXPTIME-complete problem with relevant applications in controller synthesis and a myriad of artificial…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Parity constraints, common in application domains such as circuit verification, bounded model checking, and logical cryptanalysis, are not necessarily most efficiently solved if translated into conjunctive normal form. Thus, specialized…
In this paper, we investigate the proof complexity of a wide range of substructural systems. For any proof system $\mathbf{P}$ at least as strong as Full Lambek calculus, $\mathbf{FL}$, and polynomially simulated by the extended Frege…
We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…