A Policy Iteration Algorithm for Computing Fixed Points in Static Analysis of Programs

Abstract

Abstract. We present a new method for solving the fixed point equations that appear in the static analysis of programs by abstract interpretation. We introduce and analyze a policy iteration algorithm for monotone self-maps of complete lattices. We apply this algorithm to the particular case of lattices arising in the interval abstraction of values of variables. We demonstrate the improvements in terms of speed and precision over existing techniques based on Kleene iteration, including traditional widening/narrowing acceleration mecanisms.

Template-Based Unbounded Time Verification of Affine Hybrid Automata

“…For that we use the following fixpoint transfer lemma: ∨ F V,I, • cl)). 6 Putting everything together, we obtain our main result for the time elapse operation: Abstract Semantics. So far, we have ignored the discrete transitions.…”

“…The approach of Gawlitza and Seidl [10] and the approach we present in this paper are both based on maxstrategy iteration. Costan et al [6] were the first who suggested to use strategy iteration for computing numerical invariants (for instance w.r.t. to template polyhedra).…”

“…Strategy iteration can be seen as an alternative to the traditional widening/narrowing approach of Cousot and Cousot [7]. For more information regarding these approaches see Adjé et al [1,2], Costan et al [6], Gaubert et al [9], Gawlitza and Seidl [10,11,12], Gawlitza and Monniaux [13], Gawlitza and Seidl [14,15].…”

“…Their work is focused on studying the time elapse operation for affine hybrid automata over template polyhedra, since this is a challenging problem in hybrid systems verification. They in particular adapted the min-strategy iteration approach of Costan et al [6] in order to compute a small template polyhedron that safely over-approximates the set of states reachable by continuous evolution. at a single location.…”

Abstract acceleration in linear relation analysis

“…In the lattice of intervals, the problem is studied in [57], [26] and [33]. [53] proposes a direct method to solve polyhedra fixpoint equations through the use of Farkas lemma and quantifier elimi-nation.…”