Related papers: Information in propositional proofs and algorithmi…
This short paper describes a numerical method for optimising the conservative confidence bound on the reliability of a system based on tests of its individual components. This is an alternative to the algorithmic approaches identified in…
This paper is a structured introduction to Light Affine Logic, and to its intuitionistic fragment. Light Affine Logic has a polynomially costing cut elimination (P-Time correctness), and encodes all P-Time Turing machines (P-Time…
In order to find out the limiting speed of solving a specific problem using computer, this essay provides a method based on information entropy. The relationship between the minimum computational complexity and information entropy change is…
We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a…
In recent years much effort was put into developing polynomial-time conditional lower bounds for algorithms and data structures in both static and dynamic settings. Along these lines we suggest a framework for proving conditional lower…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-gradient method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is…
Current research on the \textit{Decompose-Then-Verify} paradigm for evaluating the factuality of long-form text typically treats decomposition and verification in isolation, overlooking their interactions and potential misalignment. We find…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…
Evaluating query predicates on data samples is the only way to estimate their selectivity in certain scenarios. Finding a guaranteed optimal query plan is not a reasonable optimization goal in those cases as it might require an infinite…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
In this paper, we study reinforcement learning (RL) algorithms to solve real-world decision problems with the objective of maximizing the long-term reward as well as satisfying cumulative constraints. We propose a novel first-order policy…
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…
We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including excess entropy, Bialek et al.'s…
Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in…
Automated fact verification plays an essential role in fostering trust in the digital space. Despite the growing interest, the verification of temporal facts has not received much attention in the community. Temporal fact verification…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…