On complexity of grammars related to the safety problem

  • Authors:
  • Tomasz Jurdziński

  • Affiliations:
  • Institute of Computer Science, Wrocław University, Wrocław, Poland

  • Venue:
  • ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
  • Year:
  • 2006

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Abstract

Leftist grammars were introduced by Motwani et. al., who established the relationship between the complexity of accessibility problem (or safety problem) for certain general protection system and the membership problem of these grammars. The membership problem for leftist grammars is decidable. This implies the decidability of the accessibility problem. It is shown that the membership problem for leftist grammars is PSPACE-hard. Therefore, the accessibility problem in the appropriate protection systems is PSPACE-hard as well. Furthermore, the PSPACE-hardness result is adopted to very restricted class of leftist grammars, if the grammar is a part of the input