Related papers: GADTs, Functoriality, Parametricity: Pick Two
Attack trees (ATs) are popular graphical models for reasoning about the security of complex systems, allowing for the quantification of risk through so-called AT metrics. A large variety of different such AT metrics have been proposed, and…
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…
A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper…
As the computational footprint of modern NLP systems grows, it becomes increasingly important to arrive at more efficient models. We show that by employing graph convolutional document representation, we can arrive at a question answering…
How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis…
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
This paper studies a difference between Binary Decision Diagrams (BDDs) and Zero-suppressed BDDs (ZDDs) from a conceptual point of view. It is commonly understood that a BDD is a representation of a Boolean function, whereas a ZDD is a…
Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…
Advancing artificial intelligence for physical sciences requires representations that are both interpretable and compatible with the underlying laws of nature. We introduce METASTRINGS, a symbolic language for photonics that expresses…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared…
In the paper the problem of verification of functional programs (FPs) over strings is considered, where specifications of properties of FPs are defined by other FPs, and a FP S1 meets a specification defined by another FP S2 iff a…
This paper shows how DATR, a widely used formal language for lexical knowledge representation, can be used to define an LTAG lexicon as an inheritance hierarchy with internal lexical rules. A bottom-up featural encoding is used for LTAG…
Program source code contains complex structure information, which can be represented in structured data forms like trees or graphs. To acquire the structural information in source code, most existing researches use abstract syntax trees…
GP 2 is a non-deterministic programming language for computing by graph transformation. One of the design goals for GP 2 is syntactic and semantic simplicity, to facilitate formal reasoning about programs. In this paper, we demonstrate with…
Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide…
Many algorithms use concrete data types with some additional invariants. The set of values satisfying the invariants is often a set of representatives for the equivalence classes of some equational theory. For instance, a sorted list is a…
Ontology matching is defined as finding a relationship or correspondence between two or more entities in two or more ontologies. To solve the interoperability problem of the domain ontologies, semantically similar entities in these…
The method of constructing of Grothendieck's topology basing on a neighbourhood grammar, defined on the category of syntax diagrams is described in the article. Syntax diagrams of a formal language are the multigraphs with nodes, signed by…