Related papers: Unification of Deterministic Higher-Order Patterns…
Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we…
We present a unification problem based on first-order syntactic unification which ask whether every problem in a schematically-defined sequence of unification problems is unifiable, so called loop unification. Alternatively, our problem may…
We show the diagonal problem for higher-order pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable. From recent work by Zetzsche this means that we can construct the downward closure of the set of words…
In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs,…
New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order…
We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and…
Conventionally, data driven identification and control problems for higher order dynamical systems are solved by augmenting the system state by the derivatives of the output to formulate first order dynamical systems in higher dimensions.…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
The unification problem in a normal modal logic is to determine, given a formula F, whether there exists a substitution s such that s(F) is in that logic. In that case, s is a unifier of F. We shall say that a set of unifiers of a unifiable…
We provide a thorough construction of a system of compatible determinant line bundles over spaces of Fredholm operators, fully verify that this system satisfies a number of important properties, and include explicit formulas for all…
The univalence axiom expresses the principle of extensionality for dependent type theory. However, if we simply add the univalence axiom to type theory, then we lose the property of canonicity - that every closed term computes to a…
Fixed-parameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixed-parameter algorithms are appealing…
We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total…
We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…
A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…