By R Cooke, K L. Lockett, J A Bellman
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TACAS 2008. LNCS, vol. 4963, pp. 265–281. Springer, Heidelberg (2008) 30 F. Alberti, S. Ghilardi, and N. Sharygina 19. : Complexity of solvable cases of the decision problem for the predicate calculus. In: 19th Ann. Symp. on Found. of Comp. Sci. pp. 35–47. IEEE (1978) 20. : DPLL(T) with Exhaustive Theory Propagation and Its Application to Diﬀerence Logic. K. ) CAV 2005. LNCS, vol. 3576, pp. 321–334. Springer, Heidelberg (2005) 21. : A superexponential upper bound on the complexity of Presburger arithmetic.
A transition formula is a formula of T of the kind τ (v, v ) where v is obtained from copying the variables in v and adding a prime to each of them. For the purpose of this work, programs will be represented by their control-ﬂow automaton. 24 F. Alberti, S. Ghilardi, and N. Sharygina linit τ1 τ2 procedure initEven ( a[N ] , v ) : l1 for (i = 0; i < N ; i = i + 2) a[i] = v; l2 for (i = 0; i < N ; i = i + 2) assert(a[i] = v); (a) l1 τ3 τ4 l2 τ5 τE l3 lerror (b) Fig. 1. The initEven procedure (a) and its control-ﬂow graph (b) Deﬁnition 1 (Programs).
The (unbounded) reachability problem for a program P is to detect if P admits a feasible error path. Proving the safety of P, therefore, means solving the Decision Procedures for Flat Array Properties 25 reachability problem for P. This problem, given well known limiting results, is not decidable for an arbitrary program P. , ). To gain decidability, we must ﬁrst impose restrictions on the shape of the transition formulæ, for instance we can constrain the analysis to formulæ falling within decidable classes like those we analyzed in the previous section.
Algorithms, graphs, and computers by R Cooke, K L. Lockett, J A Bellman