A/-TERM REDUCTIONS (

The Composition Lemma for $n$-dependence

We prove that a relation obtained by composing arbitrary functions of arity $\leq k$ with a relation definable in an $n$-dependent structure is $kn$-dependent. This confirms a conjecture of Chernikov and Hempel. We also demonstrate optimality of the result.

A strengthening of the MCFL-ness of $O_2$

This work focuses on a recent proof of the fact that $O_2$ is a multiple context-free grammar (MCFG) in terms of factorizations of string tuples, and gives a new result with a stronger characterization of such factorizations than in existing theorems.

Lecture 7: The Polynomial-Time Hierarchy

The discussion of space-bounded nondeterminism is discussed and the theorem that NSPACE is closed under complement is shown, followed by introducing polynomial-time hierarchy and proving some of its basic properties.

The Complexity of Computing the Permanent

The algebraic properties of the ℱ-limit

In this article, we investigate various algebraic properties of the ℱ-limit, where ℱ is a filter on the set of natural numbers ℕ. More precisely, we study its behavior under ideal-theoretic operations, as well as its interaction with structural properties of commutative rings and its connection to the ultraproduct cons...

topologies on and arithmetic applications