Proving Safety with Trace Automata and Bounded Model Checking

Loop under-approximation is a technique that enriches C programs with additional branches that represent the effect of a (limited) range of loop iterations. While this technique can speed up the detection of bugs significantly, it introduces redundant execution traces which may complicate the verification of the program. This holds particularly true for verification tools based on Bounded Model Checking, which incorporate simplistic heuristics to determine whether all feasible iterations of a loop have been considered. We present a technique that uses \emph{trace automata} to eliminate redundant executions after performing loop acceleration. The method reduces the diameter of the program under analysis, which is in certain cases sufficient to allow a safety proof using Bounded Model Checking. Our transformation is precise---it does not introduce false positives, nor does it mask any errors. We have implemented the analysis as a source-to-source transformation, and present experimental results showing the applicability of the technique

Zero-temperature generalized phase diagram of the 4d transition metals under pressure

We use an accurate implementation of density functional theory (DFT) to calculate the zero-temperature generalized phase diagram of the 4$d$ series of transition metals from Y to Pd as a function of pressure $P$ and atomic number $Z$. The implementation used is full-potential linearized augmented plane waves (FP-LAPW), and we employ the exchange-correlation functional recently developed by Wu and Cohen. For each element, we obtain the ground-state energy for several crystal structures over a range of volumes, the energy being converged with respect to all technical parameters to within $\sim 1$ meV/atom. The calculated transition pressures for all the elements and all transitions we have found are compared with experiment wherever possible, and we discuss the origin of the significant discrepancies. Agreement with experiment for the zero-temperature equation of state is generally excellent. The generalized phase diagram of the 4$d$ series shows that the major boundaries slope towards lower $Z$ with increasing $P$ for the early elements, as expected from the pressure induced transfer of electrons from $sp$ states to $d$ states, but are almost independent of $P$ for the later elements. Our results for Mo indicate a transition from bcc to fcc, rather than the bcc-hcp transition expected from $sp$-$d$ transfer.Comment: 28 pages and 10 figures. Submitted to Phys. Rev.

Quasi-Exact Solvability and the direct approach to invariant subspaces

We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: an interesting generalization of the Lam\'e potential which posses four algebraic sectors, and a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.Comment: 17 pages, 3 figure

Phase Transition in a Random Fragmentation Problem with Applications to Computer Science

We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x_0. The process stops when all the fragments have sizes smaller than x_0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m=m_c. For m<m_c, the fluctuations are Gaussian where as for m>m_c they are anomalously large and non-Gaussian. We apply this general result to analyze two different search algorithms in computer science.Comment: 5 pages RevTeX, 3 figures (.eps

Convex Hull of Arithmetic Automata

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata

Autonomic Cluster Management System (ACMS): A Demonstration of Autonomic Principles at Work

Cluster computing, whereby a large number of simple processors or nodes are combined together to apparently function as a single powerful computer, has emerged as a research area in its own right. The approach offers a relatively inexpensive means of achieving significant computational capabilities for high-performance computing applications, while simultaneously affording the ability to. increase that capability simply by adding more (inexpensive) processors. However, the task of manually managing and con.guring a cluster quickly becomes impossible as the cluster grows in size. Autonomic computing is a relatively new approach to managing complex systems that can potentially solve many of the problems inherent in cluster management. We describe the development of a prototype Automatic Cluster Management System (ACMS) that exploits autonomic properties in automating cluster management

On computing fixpoints in well-structured regular model checking, with applications to lossy channel systems

We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual convergence of fixpoint computations. In particular, we are able to directly obtain several new decidability results on lossy channel systems.Comment: 16 page

The Isomorphism Relation Between Tree-Automatic Structures

An $\omega$-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for $\omega$-tree-automatic structures. We prove first that the isomorphism relation for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is neither a $\Sigma_2^1$-set nor a $\Pi_2^1$-set