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Proving super-polynomial size lower bounds for syntactic multilinear Algebraic Branching Programs(smABPs) computing an explicit polynomial is a challenging problem in Algebraic Complexity Theory. The order in which variables in…

Computational Complexity · Computer Science 2019-01-15 C. Ramya , B. V. Raghavendra Rao

We prove the first polynomial separation between randomized and deterministic time-space tradeoffs of multi-output functions. In particular, we present a total function that on the input of $n$ elements in $[n]$, outputs $O(n)$ elements,…

Computational Complexity · Computer Science 2023-06-29 Huacheng Yu , Wei Zhan

We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…

Computational Complexity · Computer Science 2016-09-01 Andras Farago

Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity…

Computational Complexity · Computer Science 2009-07-24 V. Arvind , Pushkar S. Joglekar , Srikanth Srinivasan

The input domain of software systems can typically be divided into sub-domains for which the outputs are similar. To ensure high quality it is critical to test the software on the boundaries between these sub-domains. Consequently, boundary…

Software Engineering · Computer Science 2022-07-20 Felix Dobslaw , Robert Feldt , Francisco de Oliveira Neto

Mean Average Precision (mAP) has been widely used for evaluating the quality of object detectors, but an efficient implementation is still absent. Current implementations can only count true positives (TP's) and false positives (FP's) for…

Computer Vision and Pattern Recognition · Computer Science 2022-06-22 Beinan Wang

An oblivious computation is one that is free of direct and indirect information leaks, e.g., due to observable differences in timing and memory access patterns. This paper presents Lambda Obliv, a core language whose type system enforces…

Programming Languages · Computer Science 2019-11-14 David Darais , Ian Sweet , Chang Liu , Michael Hicks

Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of…

Data Structures and Algorithms · Computer Science 2023-11-16 Misha Ivkov , Tselil Schramm

For every constant $d$, we design a subexponential time deterministic algorithm that takes as input a multivariate polynomial $f$ given as a constant depth algebraic circuit over the field of rational numbers, and outputs all irreducible…

Computational Complexity · Computer Science 2023-09-19 Mrinal Kumar , Varun Ramanathan , Ramprasad Saptharishi

In this paper we prove a space lower bound of $n^{\Omega(k)}$ for non-deterministic (syntactic) read-once branching programs ({\sc nrobp}s) on functions expressible as {\sc cnf}s with treewidth at most $k$ of their primal graphs. This lower…

Computational Complexity · Computer Science 2015-07-28 Igor Razgon

Determining I/O lower bounds is a crucial step in obtaining communication-efficient parallel algorithms, both across the memory hierarchy and between processors. Current approaches either study specific algorithms individually, disallow…

The bilinear assignment problem (BAP) is a generalization of the well-known quadratic assignment problem (QAP). In this paper, we study the problem from the computational analysis point of view. Several classes of neigborhood structures are…

Data Structures and Algorithms · Computer Science 2017-09-12 Vladyslav Sokol , Ante Ćustić , Abraham P. Punnen , Binay Bhattacharya

In this work we study oblivious complexity classes. These classes capture the power of interactive proofs where the prover(s) are only given the input size rather than the actual input. In particular, we study the connections between the…

Computational Complexity · Computer Science 2025-10-20 Karthik Gajulapalli , Zeyong Li , Ilya Volkovich

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN…

Machine Learning · Computer Science 2025-08-27 Rudy Bunel , Jingyue Lu , Ilker Turkaslan , Philip H. S. Torr , Pushmeet Kohli , M. Pawan Kumar

Learning to perform abstract reasoning often requires decomposing the task in question into intermediate subgoals that are not specified upfront, but need to be autonomously devised by the learner. In Raven Progressive Matrices (RPM), the…

Artificial Intelligence · Computer Science 2024-03-08 Jakub Kwiatkowski , Krzysztof Krawiec

We present a single, common tool to strictly subsume all known cases of polynomial time blackbox polynomial identity testing (PIT) that have been hitherto solved using diverse tools and techniques. In particular, we show that polynomial…

Computational Complexity · Computer Science 2011-11-03 Manindra Agrawal , Chandan Saha , Ramprasad Saptharishi , Nitin Saxena

The series-parallel (active) redundancy allocation problem with mixed components (RAP) involves setting reliable objectives for components or subsystems to meet the resource consumption constraint, e.g., the total cost. RAP has been an…

Discrete Mathematics · Computer Science 2022-04-12 Wei-Chang Yeh

Verifying the robustness of machine learning models against evasion attacks at test time is an important research problem. Unfortunately, prior work established that this problem is NP-hard for decision tree ensembles, hence bound to be…

Machine Learning · Computer Science 2023-11-14 Stefano Calzavara , Lorenzo Cazzaro , Giulio Ermanno Pibiri , Nicola Prezza

In this paper, an original reduction algorithm for solving simultaneous multivariate polynomial equations is presented. The algorithm is exponential in complexity, but the well-known algorithms, such as the extended Euclidean algorithm and…

General Mathematics · Mathematics 2021-06-01 Duggirala Meher Krishna , Duggirala Ravi

It is known that there are classes of 2-CNFs requiring exponential size non-deterministic read-once branching programs to compute them. However, to the best of our knowledge, there are no superpolynomial lower bounds for branching programs…

Computational Complexity · Computer Science 2016-05-17 Igor Razgon