Related papers: The complexity of satisfaction problems in reverse…
Given the emergent reasoning abilities of large language models, information retrieval is becoming more complex. Rather than just retrieve a document, modern information retrieval systems advertise that they can synthesize an answer based…
In this thesis, we investigate the computational content and the logical strength of Ramsey's theorem and its consequences. For this, we use the frameworks of reverse mathematics and of computable reducibility. We proceed to a systematic…
The constraint satisfaction problem (CSP) on a relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the…
We study the reverse mathematics of the theory of countable second-countable topological spaces, with a focus on compactness. We show that the general theory of such spaces works as expected in the subsystem $\mathsf{ACA}_0$ of second-order…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…
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…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
For $n\geq 3$, let $(H_n, E)$ denote the $n$-th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on $n$ vertices. We show that for all…
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…
We study the complexity of the valued constraint satisfaction problem (VCSP) for every valued structure with the domain ${\mathbb Q}$ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to…
We study the complexity of infinite-domain constraint satisfaction problems: our basic setting is that a complexity classification for the CSPs of first-order expansions of a structure $\mathfrak A$ can be transferred to a classification of…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…
Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between…
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
We say that a list of real numbers is "symmetrically realisable" if it is the spectrum of some (entrywise) nonnegative symmetric matrix. The Symmetric Nonnegative Inverse Eigenvalue Problem (SNIEP) is the problem of characterising all…
The enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic. In this setting, called reverse mathematics, one investigates which theorems provably imply which others in a…