Katsuhiko Nakamura

Synthesizing Context Free Grammars from Sample Strings Based on Inductive CYK Algorithm

This paper describes a method of synthesizing context free grammars from positive and negative sample strings, which is implemented in a grammatical inference system called Synapse. The method is based on incremental learning for positive samples and a rule generation method by “inductive CYK algorithm,” which generates minimal production rules required for parsing positive samples. Synapse can generate unambiguous grammars as well as ambiguous grammars. Some experiments showed that Synapse can synthesize several simple context free grammars in considerably short time.

Incremental learning of context free grammars by bridging rule generation and search for semi-optimum rule sets

This paper describes novel methods of learning general context free grammars from sample strings, which are implemented in Synapse system. Main features of the system are incremental learning, rule generation based on bottom-up parsing of positive samples, and search for rule sets. From the results of parsing, a rule generation process, called “bridging,” synthesizes the production rules that make up any lacking parts of an incomplete derivation tree for each positive string. To solve the fundamental problem of complexity for learning CFG, we employ methods of searching for non-minimum, semi-optimum sets of rules as well as incremental learning based on related grammars. One of the methods is search strategy called “serial search,” which finds additional rules for each positive sample and not to find the minimum rule set for all positive samples as in global search. The other methods are not to minimize nonterminal symbols in rule generation and to restrict the form of generated rules. The paper shows experimental results and compares various synthesis methods.

Towards Machine Learning of Grammars and Compilers of Programming Languages

This paper discusses machine learning of grammars and compilers of programming languages from samples of translation from source programs into object codes. This work is an application of incremental learning of definite clause grammars (DCGs) and syntax directed translation schema (SDTS), which is implemented in the Synapse system. The main experimental result is that Synapse synthesized a set of SDTS rules for translating extended arithmetic expressions with function calls and assignment operators into object codes from positive and negative samples of the translation. The object language is a simple intermediate language based on inverse Polish notation. These rules contain an unambiguous context free grammar for the extended arithmetic expressions, which specifies the precedence and associativity of the operators. This approach can be used for designing and implementing a new programming language by giving the syntax and semantics in the form of the samples of the translation.

Incremental learning of cellular automata for parallel recognition of formal languages

Parallel language recognition by cellular automata (CAs) is currently an important subject in computation theory. This paper describes incremental learning of one-dimensional, bounded, one-way, cellular automata (OCAs) that recognize formal languages from positive and negative sample strings. The objectives of this work are to develop automatic synthesis of parallel systems and to contribute to the theory of real-time recognition by cellular automata. We implemented methods to learn the rules of OCAs in the Occam system, which is based on grammatical inference of context-free grammars (CFGs) implemented in Synapse. An important feature of Occam is incremental learning by a rule generation mechanism called bridging and the search for rule sets. The bridging looks for and fills gaps in incomplete space-time transition diagrams for positive samples. Another feature of our approach is that the system synthesizes minimal or semi-minimal rule sets of CAs. This paper reports experimental results on learning several OCAs for fundamental formal languages including sets of balanced parentheses and palindromes as well as the set {anbncn | n ≥ 1}.

Learning Context Free Grammars by Using SAT Solvers

In this paper, we propose a novel approach for learning context free grammars (CFGs) from positive and negative samples by solving a Boolean satisfiability problem (SAT). We encode the set of samples, together with limits on the sizes of rule sets to be synthesized as a Boolean expression. An assignment satisfying the Boolean expression contains a minimal set of rules that derives all positive samples and no negative samples. A feature of this approach is that we can synthesize the minimal set of rules in Chomsky normal form. The other feature is that our learning method reflects any improvements of SAT solvers. We present experimental results on learning CFGs for fundamental context free languages, including a set of strings composed of the equal numbers of as and bs and the set of strings over {a, b}* not of the form ww.

Real-Time Language Recognition by One-Way and Two-Way Cellular Automata

This paper discusses real-time language recognition by 1- dimensional one-way cellular automata (OCA) and two-way cellular automata (CA), focusing on limitations of the parallel recognition power. We summarize the previous researches and investigate several languages to clarify the problems on real-time language recognition power of CA and OCA. It is shown that: 1. The language {ww : w ∈ {0, l}+} cannot be recognized by OCA in real time (this proposition is derived from a pumping lemma for cyclic strings); 2. L1There are languages L ⊂ Σ+ such that LΣ* and its reversal can be recognized by CA in real time but L is not recognizable by OCA in real time; and 3. The language {w

Control of logic program execution based on the functional relations

wn : w ∈ {0, l}+, n ≥ 1}, as well as its reversal, is recognizable by CA in real time. The last result denies an Ibarra and Jiangs conjecture [8].

Towards Incremental Learning of Mildly Context-Sensitive Grammars

This paper is concerned with the use of the information about the functional relations in logic programs to eliminate unnecessary recomputation. The method can be applied to control the execution of logic programs by specifying the functional relations so that no undesirable solution is generated. Some fundamental properties of the functionality in logic programs is discussed and a condition for the applicability of a specified functional relation to a goal is shown.

Logic hypergraph grammars and context‐free hypergraph grammars

Most models in grammatical inference have been restricted to regular or context-free grammars. As a step towards learning of more powerful grammars, this paper discusses the incremental learning of Linear Indexed Grammars (LIGs) for formal languages from positive and negative sample strings. We implemented methods of learning LIGs in LIG Learner system. An important feature of LIG Learner is incremental learning through rule generation mechanism called bridging and a search for rule sets. This paper reports experimental results on learning several LIGs for fundamental mildly-context-sensitive languages including the copy language, or the set of strings of the form ww, and a set of strings representing pseudo-knots in modeling RNA, as well as some RIR (right-linear-indexed right-linear) grammars, which are restricted LIGs and equivalent to context-free grammars.

Eliminating Stack Symbols in Push-Down Automata and Linear Indexed Grammars

This paper presents an extended graph grammar, called a logic hypergraph grammar (LHG), and discusses its capabilities and parsing method. This grammar generates hypergraphs by resolution in logic programming and is intended to be a basis for analyzing and recognizing general structures by logic programming. An LHG is called a context-free hypergraph grammar (CFHG) if each production rule represents a replacement of a hyperedge by a subhypergraph. Several normal forms are presented for CFHG and for a hierarchy on subclasses of languages of CFHGs with respect to the maximum number of vertices in nonterminal hyperedges. Finally, a parsing method of LHG using Prolog is presented.