Efficient Computation of the Locally Least-Cost Insertion String for the LR Error Repair

The locally least-cost error repair scheme, originally proposed by Fischer et al. [5,6], is an error repair scheme which allows the construction of a table-driven or algorithmic error repairing parser with the insertion and deletion cost of the terminal symbols given by the compiler designers. The principal idea governing locally least-cost error repair is that an input symbol at an errordetection point may always be edited to some string which allows the parser to continue normally [3]. The deletion is performed by comparing the insertion cost of the least-cost insertion string for the error symbol and the deletion cost of the error symbol [5]. The major problem in the locally least-cost error repair is to find out the least-cost insertion terminal string to be inserted. Fischer et al. [6] presented a novel scheme and the corresponding algorithm for computing the least-cost insertion string for LL(1) parsing. Anderson and Backhouse [2] presented an alternative method. But, the formalism and algorithm are rather inefficient for the LR-based parsing--Fischer et al.'s scheme must have the closure graph for all states, and the computing formula is not expressed explicitly [5]. In this paper, the explicit formalisms and efficient algorithms for the LR-based locally least-cost insertion string are presented. They are based on the new LALR formalisms [4,7] recently proposed by the present authors, which lead to more efficient handling of CLOSURE [1].