A counter-example for “a simpler construction for showing the intrinsically exponential complexity of the circularity problem for attribute grammars”

Abstract

Jazayeri [J. ACM 28, 4 (Oct. 198 l), 7 15-7201 proposes a simpler construction for use in the proof by Jazayeri et al. [Commun. ACM 18, 12 (Dec. 1975), 697-7061 that the circularity problem for attribute grammars has inherent exponential time complexity. The simplification introduces a flaw that invalidates the proof. The flaw can be corrected, at the cost of eliminating some of the simplification claimed for the new construction.

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

“…The intrinsically exponential complexity of the circularity problem for AGs was first proved by Jazayeri et al [6], who reduced the acceptance problem of writing pushdown acceptors [10] to the circularity problem. Jazayeri [7] (and the correction by Dill [3]) tried to provide a simpler construction of AGs by reducing the acceptance problem of space-bounded alternating Turing machines [1] to the circularity problem. The acceptance problem of (polynomial) space-bounded writing pushdown acceptors and alternating Turing machines are exponential-time (EXPTIME) complete.…”

Finding circular attributes in attribute grammars

“…For example, seeJazayeri et al [1975],Jazayeri [1981],Dill [1989], andEngelfreit and Fideé [1981].Authors' addresses: M. Rodeh, Department of Computer Science, Technion, Haifa 32000, Israel, and IBM Haifa Research Lab, e-mail: rodeh@haifa.vhet.ibm.com; M. Sagiv, Department of Computer Science, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel, e-mail: sagiv@math.tau.ac.il.…”