Concrete data types and pattern-matching are salient features of modern programming languages as powerful ways of defining and manipulating data structures. Among other things (eg. abstract syntax trees, regular expressions, DNA sequences, chemistry, cellular automata), the developments of XML greatly increases the interest in more complex pattern-matching for easily writing programs transformi...

A bstract We present a basis of dimension-eight Green’s functions involving Standard Model (SM) bosonic fields, consisting 86 new operators. Rather than using algebraic identities and integration by parts, we prove the independence these interactions in momentum space, including discussion on evanescent Our results pave way for renormalising SM effective field theory (SMEFT), as well performing...

In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...

schema matching is a critical step in many applications, such as data warehouse loading, online analytical process (olap), data mining, semantic web [2] and schema integration. this task is defined for finding the semantic correspondences between elements of two schemas. recently, schema matching has found considerable interest in both research and practice. in this paper, we present a new impr...

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 and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values...

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 and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values...

Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral equations have inspired the study algebraic structures with replicating operations. To understand their combinatorial nature, we first use rooted forests multiple decoration sets to construct free Hochschild 1-cocycle conditions. Applying universal property underlying operated method Gr\"obner-Shirshov bases, then obj...

We prove that some exact geometric pattern matching problems reduce in linear time to k -SUM when the has a fixed size k. This holds real RAM model for searching similar copy of set \(k\ge 3\) points within n plane, and an affine image d+2\) d-space. As corollaries, we obtain improved algorithms decision trees two problems. In particular, they can be solved by algebraic near-linear height.