Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a Lie algebra, whose structure is reminiscent of the insertion Lie algebras of quantum field theory. We also show that the Feynman graphs of quantum field theori...

By considering constraints on the dimensions of the Lie algebra corresponding to the weight one states of Z 2 and Z 3 orbifold models arising from imposing the appropriate modular properties on the graded characters of the automorphisms on the underlying conformal field theory, we propose a set of constructions of all but one of the 71 self-dual meromorphic bosonic conformal field theories at c...

For monoids that satisfy a weak cancellation condition, it is shown that the decidability of the existential theory of word equations is preserved under graph products. Furthermore, it is shown that the positive theory of a graph product of groups can be reduced to the positive theories of those factors, which commute with all other factors, and the existential theories of the remaining factors...

This paper analyzes the genetic operations of a new evolution mechanism proposed by us for improving the capability to deal with graph-form solutions in the real world of genetic algorithms based on the theories of GAs and GPs. A prototype of graph evolution with genetic operations is implemented and applied to some graph-related systems with the Irish-student classification data. Evaluation be...

We present an approach to creating a treebank of sentences using multiple notations or linguistic theories simultaneously. We illustrate the method by annotating sentences from the Penn Treebank II in three different theories in parallel: the original PTB notation, a Functional Dependency Grammar notation, and a Government and Binding style notation. Sentences annotated with all of these theori...

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph’s nodes. Such theories, which we call annotation theories, can be used in many applications, including the formalization of argumentation, approximate reasoning...

We present simple models which exhibit some of the remarkable features expected to hold for the yet unknown non-perturbative formulation of string theories. Among these are (1) the absence of a background or embedding space for the full theory, (2) perturbative ground states (local minima of the action) having the characteristics of spaces of different dimension, (3) duality transformations bet...

The eigenspace of the adjacency matrix of a graph possesses important information about the network structure. Recent works showed the existence of line orthogonality patterns when nodes are projected into the eigenspaces of graphs by either SVD or regular eigen decomposition. Further study proved why such phenomena hold true for simple graphs using matrix perturbation theory and several graph ...

We introduce new linear time algorithms for satisfiability of binary propositional theories (2-SAT), and for recognition and satisfiability of renamable Horn theories. The algorithms are based on unit resolution, and are thus likely easier to integrate within general SAT solvers than other graph-based algorithms.