We present a general method for introducing finitely axiomatizable "minimal" two-sorted theories various subclasses of P (problems solvable in polynomial time). The two sorts are natural numbers and finite sets numbers. latter essentially the binary strings, which provide domain defining functions small complexity classes. concentrate on class TC^0, whose problems defined by uniform polynomial-size families bounded-depth Boolean circuits with majority gates. an elegant theory VTC^0...

We show that tree-like (Gentzen's calculus) <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PK</b> where all cut formulas have depth at most a constant d does not simulate cut-free . Generally, we exhibit family of sequents polynomial size proofs but requires superpolynomial even when the rule is allowed on class cut-formulas satisfies some plausible hardness assumption. This gives (in cases, conditional) negative answers to several questions from...

Abstract Detecting potholes is an ongoing problem that requires extensive investigations as significantly deteriorate urban beauty and can cause serious harm to commuters. Multiple techniques have been developed over the years address issue. However, there has no formal way define size, particularly width, of a pothole. This work presents An's mathematical definition for width arbitrary 2D pothole at point inside. Then, each calculated by taking supremum all values points in given subset We...

We introduce a finitely axiomatizable second-order theory, which is VTC/sup 0/ associated with the class FO-uniform TC/sup 0/. It consists of base theory V/sup for AC/sup reasoning together axiom NUMONES, states existence "counting array" Y any string X: ith row contains only number 1 bits up to (excluding) bit i X. notion "strong /spl Delta//sub 1//sup B/-definability" relations in and use recursive characterization (rather than functions) show that are strongly B/-definable. follows...

Several authors have independently introduced second order theories whose provably total functionals are polynomial time computable functions on strings (e.g. [4], [6] and [7]), including the first author ([3], meant to be part of [2]). In this paper we give a detailed proof bi-interpretability result between such theory Buss' bounded arithmetic, based an elegant definition multiplication due author.

This research presents the development of an intelligent transportation system utilizing drone video to automatically track and identify speeding vehicles called TRASE. The comprises multiple modules, including a YOLOv8-based detection module, BoT-SORT-based tracking adaptive speed estimation license plate recognition module. project focuses on design, implementation, evaluation these with emphasis their performance integration into cohesive pipeline. We utilize prior information road...