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Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers…
In this paper, we introduce patchwork constructions for multivariate quasi-copulas. These results appear to be new since the kind of approach has been limited to either copulas or only bivariate quasi-copulas so far. It seems that the…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
A countable structure is said to be extendible if it has the same Scott sentence as some uncountable structure. Rigid structures are not extendible. We give an example of an extendible model with a rigid elementary extension.
We show that the class of profinite duality groups is closed under group extensions provided that the kernel satisfies some finiteness condition. This extends earlier results of Pletch and of Wingberg.
Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
In this paper we study the complexity of solving a problem when a solution of a similar instance is known. This problem is relevant whenever instances may change from time to time, and known solutions may not remain valid after the change.…
A permutation of the elements of a graph is a {\it construction sequence} if no edge is listed before either of its endpoints. The complexity of such a sequence is investigated by finding the delay in placing the edges, an {\it opportunity…
We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the…
We develop a word mechanism applied in knot and link diagrams for the illustration of a diagrammatic property. We also give a necessary condition for determining incompressible and pairwise incompressible surfaces, that are embedded in knot…
Fix a set-theoretic universe $V$. We look at small extensions of $V$ as generalised degrees of computability over $V$. We also formalise and investigate the complexity of certain methods one can use to define, in $V$, subclasses of degrees…
We prove that every finite dimensional representation of a finite group over a field of characteristic p admits a finite resolution by p-permutation modules. The proof involves a reformulation in terms of derived categories.
We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…
We prove that if $B\subseteq A$ is an extension of finite dimensional algebras such that the projective dimension of $A/B$ as a $B$-bimodule is finite, if $A$ has finite finitistic dimension, then so does $B$. We exhibit examples…
In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and…