Cyclic operator precedence grammars for parallel parsing

Operator precedence languages (OPLs) enjoy the local parsability property, which means that a code fragment enclosed within a pair of markers playing the role of parentheses can be parsed with no knowledge of its external context. This property has been exploited to build parallel parsers for languages formalized as OPLs. It has been observed, however, that when the syntax trees of sentences have a linear substructure, parsing must necessarily proceed sequentially, making it ineffective to split such a subtree into chunks to be processed in parallel. This inconvenience derives from the hypothesis that the equality precedence relation cannot be cyclic, which has been so far assumed by most literature on OPLs. This hypothesis was motivated by the need to keep the mathematical notation as simple as possible, although it caused a discrepancy between the expressive power of operator precedence grammars and other formalisms defining OPLs such as operator precedence automata, monadic second order logic and operator precedence expressions, which do not assume acyclicity.We present an enriched version of operator precedence grammars, called cyclic, that allows for a simplified version of regular expressions in the right hand sides of grammar rules. For this class of operator precedence grammars the acyclicity hypothesis of the equality precedence relation is no more needed to guarantee the algebraic properties of the generated languages. The expressive power of the cyclic grammars is now fully equivalent to that of other formalisms defining OPLs. As a result, cyclic operator precedence grammars produce unranked syntax trees and sentences with flat unbounded substructures that can be naturally partitioned into chunks suitable for parallel parsing.