On exponential-time completeness of the circularity problem for attribute grammars

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 shown that the problem is EXPTIME-complete. This paper 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.