On Exponential-Time Completeness of the Circularity Problem for Attribute Grammars

TL;DR

This paper proves that the circularity problem for attribute grammars is EXPTIME-complete by constructing an alternating Turing machine that operates within polynomial space, establishing both hardness and membership.

Contribution

It provides the first proof of EXPTIME-completeness for the circularity problem in attribute grammars using an alternating Turing machine approach.

Findings

Circularity problem is EXPTIME-hard from automata theory reductions.

An alternating Turing machine with polynomial space is constructed for the problem.

The problem is shown to be in EXPTIME, establishing EXPTIME-completeness.

Abstract

Attribute grammars (AGs) are a formal technique for defining semantics of programming languages. Existing complexity proofs on the circularity problem of AGs are based on automata theory, such as writing pushdown acceptor and alternating Turing machines. They reduced the acceptance problems of above automata, which are exponential-time (EXPTIME) complete, to the AG circularity problem. These proofs thus show that the circularity problem is EXPTIME-hard, at least as hard as the most difficult problems in EXPTIME. However, none has given a proof for the EXPTIME-completeness of the problem. This paper first presents an alternating Turing machine for the circularity problem. The alternating Turing machine requires polynomial space. Thus, the circularity problem is in EXPTIME and is then EXPTIME-complete.