Graph Interpolation Grammars as Context-Free Automata

A derivation step in a Graph Interpolation Grammar has the effect of scanning an input token. This feature, which aims at emulating the incrementality of the natural parser, restricts the formal power of GIGs. This contrasts with the fact that the derivation mechanism involves a context-sensitive device similar to tree adjunction in TAGs. The combined effect of input-driven derivation and restricted context-sensitiveness would be conceivably unfortunate if it turned out that Graph Interpolation Languages did not subsume Context Free Languages while being partially context-sensitive. This report sets about examining relations between CFGs and GIGs, and shows that GILs are a proper superclass of CFLs. It also brings out a strong equivalence between CFGs and GIGs for the class of CFLs. Thus, it lays the basis for meaningfully investigating the amount of context-sensitiveness supported by GIGs, but leaves this investigation for further research

Non-Direct Encoding Method Based on Cellular Automata to Design Neural Network Architectures

Architecture design is a fundamental step in the successful application of Feed forward Neural Networks. In most cases a large number of neural networks architectures suitable to solve a problem exist and the architecture design is, unfortunately, still a human expert’s job. It depends heavily on the expert and on a tedious trial-and-error process. In the last years, many works have been focused on automatic resolution of the design of neural network architectures. Most of the methods are based on evolutionary computation paradigms. Some of the designed methods are based on direct representations of the parameters of the network. These representations do not allow scalability; thus, for representing large architectures very large structures are required. More interesting alternatives are represented by indirect schemes. They codify a compact representation of the neural network. In this work, an indirect constructive encoding scheme is proposed. This scheme is based on cellular automata representations and is inspired by the idea that only a few seeds for the initial configuration of a cellular automaton can produce a wide variety of feed forward neural networks architectures. The cellular approach is experimentally validated in different domains and compared with a direct codification scheme.Publicad

Underapproximation of Procedure Summaries for Integer Programs

We show how to underapproximate the procedure summaries of recursive programs over the integers using off-the-shelf analyzers for non-recursive programs. The novelty of our approach is that the non-recursive program we compute may capture unboundedly many behaviors of the original recursive program for which stack usage cannot be bounded. Moreover, we identify a class of recursive programs on which our method terminates and returns the precise summary relations without underapproximation. Doing so, we generalize a similar result for non-recursive programs to the recursive case. Finally, we present experimental results of an implementation of our method applied on a number of examples.Comment: 35 pages, 3 figures (this report supersedes the STTT version which in turn supersedes the TACAS'13 version

Connectionist learning of regular graph grammars

This paper presents a new connectionist approach to grammatical inference. Using only positive examples, the algorithm learns regular graph grammars, representing two-dimensional iterative structures drawn on a discrete Cartesian grid. This work is intended as a case study in connectionist symbol processing andgeometric concept formation. A grammar is represented by a self-configuring connectionist network that is analogous to a transition diagram except that it can deal with graph grammars as easily as string grammars. Learning starts with a trivial grammar, expressing nogrammatical knowledge, which is then refined, by a process of successive node splitting and merging, into a grammar adequate to describe the population of input patterns. In conclusion, I argue that the connectionist style of computation is, in some ways, better suited than sequential computation to the task of representing and manipulating recursive structures