SAT-Based Algorithms for Regular Graph Pattern Matching

Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if two graphs are identical. Despite its usefulness, the properties that one may check using graph isomorphism are rather limited, since it only allows strict equality checks between two graphs. For example, it does not allow one to check complex structural properties such as if the target graph is an arbitrary length sequence followed by an arbitrary size loop. We propose a generalization of graph isomorphism that allows one to check such properties through a declarative specification. This specification is given in the form of a Regular Graph Pattern (ReGaP), a special type of graph, inspired by regular expressions, that may contain wildcard nodes that represent arbitrary structures such as variable-sized sequences or subgraphs. We propose a SAT-based algorithm for checking if a target graph matches a given ReGaP. We also propose a preprocessing technique for improving the performance of the algorithm and evaluate it through an extensive experimental evaluation on benchmarks from the CodeSearchNet dataset.

Qualia as physical measurements: a mathematical model of qualia and pure concepts

A space of qualia is defined to be a sober topological space whose points are the qualia and whose open sets are the pure concepts in the sense of Lewis, carrying additional algebraic structure that conveys the conscious experience of subjective time and logical abstraction. This structure is analogous to that of a space of physical measurements. It is conjectured that qualia and measurements have the same nature, corresponding to fundamental processes via which classical information is produced and physically stored, and that therefore the hard problem of consciousness and the measurement problem are two facets of the same problem. The space of qualia is independent from any preexisting notions of spacetime and conscious agent, but its structure caters for a derived geometric model of observer. Intersubjectivity is based on relating different observers in a way that leads to a logical version of quantum superposition.