On Exponential-Time Completeness of the Circularity Problem for Attribute Grammars
<|reference_start|>On Exponential-Time Completeness of the Circularity Problem for Attribute Grammars: 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.<|reference_end|>
@article{wu2000on,
    title={On Exponential-Time Completeness of the Circularity Problem for
  Attribute Grammars},
    author={Pei-Chi Wu},
    journal={arXiv preprint arXiv:cs/0010015},
    year={2000},
    archivePrefix={arXiv},
    eprint={cs/0010015},
    primaryClass={cs.PL cs.CC}
}