Related papers: Proof complexity of positive branching programs
Since the breakthrough superpolynomial multilinear formula lower bounds of Raz (Theory of Computing 2006), proving such lower bounds against multilinear algebraic branching programs (mABPs) has been a longstanding open problem in algebraic…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms…
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder…
Bayesian neural networks (BNNs) can account for both aleatoric and epistemic uncertainty. However, in BNNs the priors are often specified over the weights which rarely reflects true prior knowledge in large and complex neural network…
In (Kabanets, Impagliazzo, 2004) it is shown how to decide the circuit polynomial identity testing problem (CPIT) in deterministic subexponential time, assuming hardness of some explicit multilinear polynomial family for arithmetical…
We show that if a language $L$ admits a public-coin unambiguous interactive proof (UIP) with round complexity $\ell$, where $a$ bits are communicated per round, then the batch language $L^{\otimes k}$, i.e. the set of $k$-tuples of…
We present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-integer programming (MIP). Our system generalizes the seminal work of Bogaerts, Gocht, McCreesh, and…
We study the problem of obtaining deterministic black-box polynomial identity testing algorithms (PIT) for algebraic branching programs (ABPs) that are read-once and oblivious. This class has an deterministic white-box polynomial identity…
The long run behaviour of linear dynamical systems is often studied by looking at eventual properties of matrices and recurrences that underlie the system. A basic problem that lies at the core of many questions in this setting is the…
Recent attention to relational knowledge bases has sparked a demand for understanding how relations change between entities. Petri nets can represent knowledge structure and dynamically simulate interactions between entities, and thus they…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…
Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural…
Recent work in model-agnostic explanations of black-box machine learning has demonstrated that interpretability of complex models does not have to come at the cost of accuracy or model flexibility. However, it is not clear what kind of…
Mathematical reasoning is central to artificial intelligence, with applications in education, code generation, and research-level mathematical discovery. Mathematical competitions highlight two problem types: theorem proving, requiring…
This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we…
We introduce the concept of structured synthesis for Markov decision processes where the structure is induced from finitely many pre-specified options for a system configuration. The resulting synthesis problem is in general a nonlinear…
The computational complexity of the partition, 0-1 subset sum, unbounded subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple variants were studied in numerous papers in the past where all the weights and profits were…