Abstract. Ultimate Automizer is a software verifier that generalizes proofs for traces to proofs for larger parts for the program. In recent years the portfolio of proof producers that are available to Ultimate has grown continuously. This is not only because more trace analysis algorithms have been implemented in Ultimate but also due to the continuous progress in the SMT community. In this paper we explain how Ultimate Automizer dynamically selects trace analysis algorithms and how the tool decides when proofs for traces are "good" enough for using them in the abstraction refinement. Verification ApproachUltimate Automizer (in the following called Automizer) is a software verifier that is able to check safety and liveness properties. The tool implements an automata-based [6] instance of the CEGAR scheme. In each iteration, we pick a trace (which is a sequence of statements) that leads from the initial location to the error location and check whether the trace is feasible (i.e., corresponds to an execution) or infeasible. If the trace is feasible, we report an error to the user; otherwise we compute a sequence of predicates along the trace as a proof of the trace's infeasibility. We call such a sequence of predicates a sequence of interpolants since each predicate "interpolates" between the set of reachable states and the set of states from which we cannot reach the error. In the refinement step of the CEGAR loop, we try to find all traces whose infeasibility can be shown with the given predicates and subtract these traces from the set of (potentially spurious) error traces that have not yet been analyzed. We use automata to represent sets of traces; hence the subtraction is implemented as an automata operation. The major difference to a classical CEGAR-based predicate abstraction is that we never have to do any logical reasoning (e.g., SMT solver calls) that involves predicates of different CEGAR iterations.We use this paper to explain how our tool obtains the interpolants that are used in the refinement step. The Ultimate program analysis framework

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Existing techniques for Craig interpolation for the quantifierfree fragment of the theory of arrays are inefficient for computing sequence and tree interpolants: the solver needs to run for every partitioning (A, B) of the interpolation problem to avoid creating AB-mixed terms. We present a new approach using Proof Tree Preserving Interpolation and an array solver based on Weak Equivalence on Arrays. We give an interpolation algorithm for the lemmas produced by the array solver. The computed interpolants have worst-case exponential size for extensionality lemmas and worst-case quadratic size otherwise. We show that these bounds are strict in the sense that there are lemmas with no smaller interpolants. We implemented the algorithm and show that the produced interpolants are useful to prove memory safety for C programs.

We present a molecular dynamics simulation study of the self-assembly of coarse-grained lipid molecules from unbiased random initial configurations. Our lipid model is based on a well-tried CG polymer model with an additional potential that mimics the hydrophobic properties of lipid tails. We find that several stages of self-organization of lipid clusters are involved in the dynamics of bilayer formation and that the resulting equilibrium structures sensitively depend on the strength of hydrophobic interactions hc of the lipid tails and on temperature T. The obtained stable lipid membranes are quantitatively analyzed with respect to their local structure and their degree of order. At equilibrium, we obtain self-stabilizing bilayer membrane structures that exhibit a bending stiffness κB and compression modulus KC comparable to experimental measurements under physiological conditions. We present a phase diagram of our lipid model which covers a sol-gel transition, a liquid (or gel-like) phase including stable bilayer structures and vesicle formation, as well as a quasi-crystalline phase. We also determine the exact conditions for temperature T and degree of hydrophobicity hc for stable bilayer formation including closed vesicles.

Abstract. Ultimate Taipan is a software model checker that uses trace abstraction and abstract interpretation to prove correctness of programs. In contrast to previous versions, Ultimate Taipan now uses dynamic block encoding to obtain the best precision possible when evaluating transition formulas of large block encoded programs. Verification ApproachUltimate Taipan (or Taipan for brevity) is a software model checker which combines trace abstraction [9,10] The initial abstraction of the program is an automaton with the same graph structure as the program's control flow graph, where program locations are states, transitions are labeled with program statements, and error locations are accepting. Thus, the language of the automaton consists of all traces, i.e., sequences of statements, that, if executable, lead to an error. In each iteration, the algorithm chooses a trace from the language of the current automaton and constructs a path program from it. A path program is a projection of the (abstraction of the) program to the trace. The algorithm then uses abstract interpretation to compute fixpoints for the path program. If the fixpoints of the path program are sufficient to prove correctness, i.e., the error location is unreachable, at least the chosen trace and all other traces that are covered by the path program are infeasible. The computed fixpoints constitute a proof of correctness for the path program and can be represented as a set of state assertions. From this set of state assertions, the abstraction is refined by constructing a new automaton whose language only consists of infeasible traces and then subtracting it from the current abstraction using an automatatheoretic difference operation. If abstract interpretation was unable to prove correctness of the path program, the algorithm obtains a proof of infeasibility of the trace using either interpolating SMT solvers or a combination of unsatisfiable cores and strongest post or weakest pre [6]. If the currently analyzed trace is feasible,