  The paper considers several definitions of information flow security for
intransitive policies from the point of view of the complexity of verifying
whether a finite-state system is secure. The results are as follows. Checking
(i) P-security (Goguen and Meseguer), (ii) IP-security (Haigh and Young), and
(iii) TA-security (van der Meyden) are all in PTIME, while checking TO-security
(van der Meyden) is undecidable, as is checking ITO-security (van der Meyden).
The most important ingredients in the proofs of the PTIME upper bounds are new
characterizations of the respective security notions, which also lead to new
unwinding proof techniques that are shown to be sound and complete for these
notions of security, and enable the algorithms to return simple
counter-examples demonstrating insecurity. Our results for IP-security improve
a previous doubly exponential bound of Hadj-Alouane et al.
