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The world is fundamentally compositional, so it is natural to think of visual recognition as the recognition of basic visually primitives that are composed according to well-defined rules. This strategy allows us to recognize unseen complex…
The paper gives an example of a tree language G that is recognised by an unambiguous parity automaton and is analytic-complete as a set in Cantor space. This already shows that the unambiguous languages are topologically more complex than…
We investigate machine models similar to Turing machines that are augmented by the operations of a first-order structure $\mathcal{R}$, and we show that under weak conditions on $\mathcal{R}$, the complexity class $\text{NP}(\mathcal{R})$…
We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling…
For any abelian group $G$, we classify up to isomorphism all $G$-gradings on the classical central simple Lie algebras, except those of type $D_4$, over the field of real numbers (or any real closed field).
We show that the commutative closure combined with the iterated shuffle is a regularity-preserving operation on group languages. In particular, for commutative group languages, the iterated shuffle is a regularity-preserving operation. We…
We study varieties that contain unranked tree languages over all alphabets. Trees are labeled with symbols from two alphabets, an unranked operator alphabet and an alphabet used for leaves only. Syntactic algebras of unranked tree languages…
In the first half of the present paper, we study higher-level generalizations of differential modules in positive characteristic. These objects may be regarded as ring-theoretic counterparts of vector bundles on a curve equipped with an…
Semantic parsing is the task of obtaining machine-interpretable representations from natural language text. We consider one such formal representation - First-Order Logic (FOL) and explore the capability of neural models in parsing English…
Quaternionic polynomials occur naturally in applications of quaternions in science and engineering, and normalization of quaternionic polynomials is a basic manipulation. Once a Groebner basis is certified for the defining ideal I of the…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
The notion of a difference hierarchy, first introduced by Hausdorff, plays an important role in many areas of mathematics, logic and theoretical computer science such as descriptive set theory, complexity theory, and the theory of regular…
This paper describes an automatic word classification system which uses a locally optimal annealing algorithm and average class mutual information. A new word-class representation, the structural tag is introduced and its advantages for use…
The term ``Boolean category'' should be used for describing an object that is to categories what a Boolean algebra is to posets. More specifically, a Boolean category should provide the abstract algebraic structure underlying the proofs in…
Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which…
We show that first order logic (FO) and first order logic extended with modulo counting quantifiers (FOMOD) over purely functional vocabularies which extend addition, satisfy the Crane beach property (CBP) if the logic satisfies a normal…
We classify gradings by arbitrary abelian groups on the classical simple Lie and Jordan superalgebras $Q(n)$, $n \geq 2$, over an algebraically closed field of characteristic different from $2$ (and not dividing $n+1$ in the Lie case): fine…
We prove that the join of two sets may actually fall into a lower level of the extended low hierarchy than either of the sets. In particular, there exist sets that are not in the second level of the extended low hierarchy, EL_2, yet their…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
An infinite family of Boolean polynomials which correspond to the discrete average maps, defined in [2], is constructed and their algebraic and combinatorial properties are investigated. They turn out to be balanced, and some recurrence…