Related papers: Provable better quasi orders
We study the following problem: Determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
In this paper, we study the lower complexity bounds for finite-sum optimization problems, where the objective is the average of $n$ individual component functions. We consider Proximal Incremental First-order (PIFO) algorithms which have…
Justin Moore's weak club-guessing principle $\mho$ admits various possible generalizations to the second uncountable cardinal. One of them was shown to hold in ZFC by Shelah. A stronger one was shown to follow from several consequences of…
By Lindstr\"{o}m's theorems, the expressive power of first order logic (and similarly continuous logic) is not strengthened without losing some interesting property. Weakening it, is however less harmless and has been payed attention by…
We attempt to systematically derive perturbative quantum corrections to the Berry diagonal approximation of the two-level correlation function (TLCF) for chaotic systems. To this end, we develop a ``weak diagonal approximation'' based on a…
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…
The dimension of a partial order $P$ is the minimum number of linear orders whose intersection is $P$. There are efficient algorithms to test if a partial order has dimension at most $2$. In 1982 Yannakakis showed that for $k\geq 3$ to test…
Given an uncountable regular cardinal $\kappa$, a partial order is $\kappa$-stationarily layered if the collection of regular suborders of $\mathbb{P}$ of cardinality less than $\kappa$ is stationary in $\mathcal{P}_\kappa(\mathbb{P})$. We…
We investigate the poset (P(X),\subset), where P(X) is the set of isomorphic suborders of a countable ultrahomogeneous partial order X. For X different from (resp. equal to) a countable antichain the order types of maximal chains in…
We prove that, for every cardinal number $\alpha\geq {\mathfrak c}$, there exists a metrizable space $X$ with $|X|=\alpha$ such that for every pair of quasiorders $\leq_1$, $\leq_2$ on a set $Q$ with $|Q| \leq \alpha$ satisfying the…
We construct a nonrecursive set \(A\le_T\emptyset'\) and a uniformly computable family of sets \(C_0,C_1,\dots\), all bounded finite-one equivalent to \(A\), such that the corresponding \(1\)-degrees form a copy of the dense linear order…
Let $\mathcal{C}$ be a finitely bicomplete category and $\mathcal{W}$ a subcategory. We prove that the existence of a model structure on $\mathcal{C}$ with $\mathcal{W}$ as subcategory of weak equivalence is not first order expressible.…
The aim of Reverse Mathematics(RM for short)is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. These minimal axioms are almost always equivalent to the theorem, working over the base theory of RM, a weak…
Denote by $G$ a finite group and by $\psi(G)$ the sum of element orders in $G$. If $t$ is a positive integer, denote by $C_t$ the cyclic group of order $t$ and write $\psi(t)=\psi(C_t)$. In this paper we proved the following Theorem A: Let…
A partition is finitary if all its members are finite. For a set $A$, $\mathscr{B}(A)$ denotes the set of all finitary partitions of $A$. It is shown consistent with $\mathsf{ZF}$ (without the axiom of choice) that there exist an infinite…
First-order temporal logics are notorious for their bad computational behaviour. It is known that even the two-variable monadic fragment is highly undecidable over various linear timelines, and over branching time even one-variable…
The Quantum Approximate Optimization Algorithm (QAOA) is designed to run on a gate model quantum computer and has shallow depth. It takes as input a combinatorial optimization problem and outputs a string that satisfies a high fraction of…
We compare the expressiveness of two extensions of monadic second-order logic (MSO) over the class of finite structures. The first, counting monadic second-order logic (CMSO), extends MSO with first-order modulo-counting quantifiers,…
The most successful unfolding rules used nowadays in the partial evaluation of logic programs are based on well quasi orders (wqo) applied over (covering) ancestors, i.e., a subsequence of the atoms selected during a derivation. Ancestor…