Related papers: Coalgebraic Path Constraints
The problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertex-colored temporal graph, asks for a path whose vertices have…
E-graphs are a prominent data structure that has been increasing in popularity in recent years due to their expanding range of applications in various formal reasoning tasks. Often, they are used for equality saturation, a process of…
The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this…
Considering an extension of the principle of covarience to the action along a path in relativistic Lagrangian mechanics, we motivate the use of geometric -- i.e. covariant and parameter invariant -- Lagrangian functions. We then study some…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…
We study rational modules over complete path and monomial algebras, and the problem of when rational modules over the dual $C^*$ of a coalgebra $C$ are closed under extensions, equivalently, when is the functor $Rat$ a torsion functor. We…
We revisit our earlier work on the representation of quantum systems as Chu spaces, and investigate the use of coalgebra as an alternative framework. On the one hand, coalgebras allow the dynamics of repeated measurement to be captured, and…
The motivation of this paper is to construct a deformation theory of coderivations of coassociative coalgebras. We introduce a notion of a Coder pair, that is, a coassociative coalgebra with a coderivation. Then we define a proper…
We provide a construction of the fixed points of functors which may not be inital algebras or final coalgebras. For an endofunctor F, this fixed point construction may be expressed as a pair of adjoint functors between F-coalgebras and…
In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…
In this work, we propose a class of equational theories for bounded binary circuits that have the finite variant property. These theories could serve as a building block to specify cryptographic primitive implementations and automatically…
For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper…
Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for…
In this paper, we investigate the many-valued version of coalgebraic modal logic through predicate lifting approach. Coalgebras, understood as generic transition systems, can serve as semantic structures for various kinds of modal logics. A…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
We combine the theory of inductive data types with the theory of universal measurings. By doing so, we find that many categories of algebras of endofunctors are actually enriched in the corresponding category of coalgebras of the same…
Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to…
An introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones.…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…