Related papers: Optimal Satisfiability Checking for Arithmetic $\m…
Parallelization is a popular strategy for improving the performance of iterative algorithms. Optimization methods are no exception: design of efficient parallel optimization methods and tight analysis of their theoretical properties are…
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
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…
Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…
We study calibeating, the problem of post-processing external forecasts online to minimize cumulative losses and match an informativeness-based benchmark. Unlike prior work, which analyzed calibeating for specific losses with specific…
Chain-of-Thought (CoT) prompting has shown promise in enhancing the reasoning capabilities of large language models (LLMs) by generating natural language (NL) rationales that lead to the final answer. However, it struggles with numerical…
Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…
This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for…
Machine learning models support decision-making, yet the reasons behind their predictions are opaque. Clear and reliable explanations help users make informed decisions and avoid blindly trusting model outputs. However, many existing…
We present GoldbachGPU, an open-source framework for large-scale computational verification of Goldbach's conjecture using commodity GPU hardware. Prior GPU-based approaches reported a hard memory ceiling near 10^11 due to monolithic…
Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…
Satisfiability-based automated reasoning is an approach that is being successfully used in software engineering to validate complex software, including for safety-critical systems. Such reasoning underlies many validation activities, from…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
This paper introduces bucket calculus, a novel mathematical framework that fundamentally transforms the computational complexity landscape of parallel machine scheduling optimization. We address the strongly NP-hard problem…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
We develop a sound, complete and practically implementable tableaux-based decision method for constructive satisfiability testing and model synthesis in the fragment ATL+ of the full Alternating time temporal logic ATL*. The method extends…
We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…
An improved Present Future form (PF form) for linear time $\mu$-calculus ($\nu$TL) is presented in this paper. In particular, the future part of the new version turns into the conjunction of elements in the closure of a formula. We show…
We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…
Many problems in static program analysis can be modeled as the context-free language (CFL) reachability problem on directed labeled graphs. The CFL reachability problem can be generally solved in time $O(n^3)$, where $n$ is the number of…