Related papers: Punctual equivalence relations and their (punctual…
We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for…
A path query extracts vertex tuples from a labeled graph, based on the words that are formed by the paths connecting the vertices. We study the computational complexity of measuring the contribution of edges and vertices to an answer to a…
In this article, we introduce a notion of reducibility for partial functions on the natural numbers, which we call subTuring reducibility. One important aspect is that the subTuring degrees correspond to the structure of the realizability…
One of the well-known results in concurrency theory concerns the relationship between event structures and occurrence nets: an occurrence net can be associated with a prime event structure, and vice versa. More generally, the relationships…
Satisfiability problems play a central role in computer science and engineering as a general framework for studying the complexity of various problems. Schaefer proved in 1978 that truth satisfaction of propositional formulas given a…
Following a line of research initiated in \cite{BBNN}, I describe a general framework for turning reduction concepts of relative computability into diagrams forming an analogy with the Cicho\'n diagram for cardinal characteristics of the…
Multi-valued functions are common in computable analysis (built upon the Type 2 Theory of Effectivity), and have made an appearance in complexity theory under the moniker search problems leading to complexity classes such as PPAD and PLS…
We identify a notion of reducibility between predicates, called instance reducibility, which commonly appears in reverse constructive mathematics. The notion can be generally used to compare and classify various principles studied in…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an $\omega$-Erdos cardinal, we determine which of these theories are Borel complete. We develop machinery,…
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
Event structures have emerged as a foundational model for concurrent computation, explaining computational processes by outlining the events and the relationships that dictate their execution. They play a pivotal role in the study of key…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
The formalization of process algebras usually starts with a minimal core of operators and rules for its transition system, and then relax the system to improve its usability and ease the proofs. In the calculus of communicating systems…
We introduce and study several notions of computability-theoretic reducibility between subsets of $\omega$ that are "robust" in the sense that if only partial information is available about the oracle, then partial information can be…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
This paper compares different representations (in the sense of computable analysis) of a number of function spaces that are of interest in analysis. In particular subspace representations inherited from a larger function space are compared…
We are dealing with the complexity of the homeomorphism equivalence relation on some classes of metrizable compacta from the viewpoint of invariant descriptive set theory. We prove that the homeomorphism equivalence relation of absolute…