On the succinctness of RoCTL

  • Authors:

  • John C. McCabe-Dansted

  • Affiliations:

  • University of Western Australia, Crawley, Perth Western Australia

  • Venue:
  • CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
  • Year:
  • 2011

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Abstract

It can be desirable to specify policies that require a system to achieve some outcome even if a certain number of failures occur. The temporal logic of robustness RoCTL* extends CTL* with operators from Deontic logic, and a novel operator referred to as "Robustly" (French, McCabe-Dansted & Reynolds 2007). It is known that RoCTL* can be translated into CTL*, but that the translation must be have at least a singly exponential blowup per nested Robustly operator (McCabe-Dansted, Pinchinat, French & Reynolds 2009). We now present a translation that has asymptotically a singly exponential blowup per nested Robustly operator, matching the known lower bound. This translation uses a combination of automata and LTL. This combination is useful not due to greater theoretical expressivity than LTL, but instead because RoCTL* is more naturally expressed combination of automaton and LTL operators than LTL operators alone; this combination allows us to avoid the need for a round trip from automata to LTL and back for each nested Robustly operator.