Related papers: Computability for tree presentations of continuum-…
The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese (1991). We prove the following problem is decidable: Input: (i) A monadic second…
We establish a computation-substrate-agnostic inference architecture in which domain is an explicit first-class computational parameter. This produces domain-scoped pruning that reduces per-query search space from O(N) to O(N/K),…
We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively unform-, order-, and $\sigma$-order convergence,…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has…
A Concept Tree is a structure for storing knowledge where the trees are stored in a database called a Concept Base. It sits between the highly distributed neural architectures and the distributed information systems, with the intention of…
Graceful tree conjecture is a well-known open problem in graph theory. Here we present a computational approach to this conjecture. An algorithm for finding graceful labelling for trees is proposed. With this algorithm, we show that every…
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…
A celebrated result by M. Davis, H. Putnam, J. Robinson, and Y. Matiyasevich shows that a set of integers is listable if and only if it is positive existentially definable in the language of arithmetic. We investigate analogues of this…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
The finite satisfiability problem for the two-variable fragment of first-order logic interpreted over trees was recently shown to be ExpSpace-complete. We consider two extensions of this logic. We show that adding either additional binary…
Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
A computable ring is a ring equipped with mechanical procedure to add and multiply elements. In most natural computable integral domains, there is a computational procedure to determine if a given element is prime/irreducible. However,…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
Combinatorial trees can be used to represent genealogies of asexual individuals. These individuals can be endowed with birth and death times, to obtain a so-called `chronological tree'. In this work, we are interested in the continuum…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
A compact set has computable type if any homeomorphic copy of the set which is semicomputable is actually computable. Miller proved that finite-dimensional spheres have computable type, Iljazovi\'c and other authors established the property…