UNITY and Büchi automata

UNITY is a model for concurrent specifications with a complete logic for proving progress properties of the form ``$P$ leads to $Q$''. UNITY is generalized to U-specifications by giving more freedom to specify the steps that are to be taken infinitely often. In particular, these steps can correspond to non-total relations. The generalization keeps the logic sound and complete. The paper exploits the generalization in two ways. Firstly, the logic remains sound when the specification is extended with hypotheses of the form ``$F$ leads to $G$''. As the paper shows, this can make the logic incomplete. The generalization is used to show that the logic remains complete, if the added hypotheses ``$F$ leads to $G$'' satisfy ``$F$ unless $G$''. The main result extends the applicability and completeness of UNITY logic to proofs that a given concurrent program satisfies any given formula of LTL, linear temporal logic, without the next-operator which is omitted because it is sensitive to stuttering. For this purpose, the program, written as a UNITY program, is extended with a number of boolean variables. The proof method relies on implementing the LTL formula, i.e., restricting the specification in such a way that only those runs remain that satisfy the formula. This result is a variation of the classical construction of a B\"uchi automaton for a given LTL formula that accepts precisely those runs that satisfy the formula

Trylock, a case for temporal logic and eternity variables

An example is given of a software algorithm that implements its specification in linear time temporal logic (LTL), but not in branching time temporal logic (CTL). In LTL, a prophecy of future behaviour is needed to prove the simulation. Eternity variables are used for this purpose. The final phase of the proof is a refinement mapping in which two threads exchange roles. The example is a software implementation of trylock in a variation of the fast mutual exclusion algorithm of Lamport (1987). It has been used fruitfully for the construction of software algorithms for high performance mutual exclusion

MCSH, a lock with the standard interface

The MCS lock of Mellor-Crummey and Scott (1991), 23 pages. is a very efficient first-come first-served mutual-exclusion algorithm that uses the atomic hardware primitives fetch-and-store and compare-and-swap. However, it has the disadvantage that the calling thread must provide a pointer to an allocated record. This additional parameter violates the standard locking interface, which has only the lock as a parameter. Hence, it is impossible to switch to MCS without editing and recompiling an application that uses locks.This article provides a variation of MCS with the standard interface, which remains FCFS, called MCSH. One key ingredient is to stack allocate the necessary record in the acquire procedure of the lock, so its life-time only spans the delay to enter a critical section. A second key ingredient is communicating the allocated record between the acquire and release procedures through the lock to maintain the standard locking interface. Both of these practices are known to practitioners, but our solution combines them in a unique way. Furthermore, when these practices are used in prior papers, their correctness is often argued informally. The correctness of MCSH is verified rigorously with the proof assistant PVS, and experiments are run to compare its performance with MCS and similar locks

Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian

We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed $K_C$-orbits in the Lagrangian Grassmannian as the categorical quotient. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent $K_C$-orbits, which is a "quotient" of the resolution of the null fiber.Comment: 17 pages; completely revised and add reference

Nonequilibrium spectral diffusion due to laser heating in stimulated photon echo spectroscopy of low temperature glasses

A quantitative theory is developed, which accounts for heating artifacts in three-pulse photon echo (3PE) experiments. The heat diffusion equation is solved and the average value of the temperature in the focal volume of the laser is determined as a function of the 3PE waiting time. This temperature is used in the framework of nonequilibrium spectral diffusion theory to calculate the effective homogeneous linewidth of an ensemble of probe molecules embedded in an amorphous host. The theory fits recently observed plateaus and bumps without introducing a gap in the distribution function of flip rates of the two-level systems or any other major modification of the standard tunneling model.Comment: 10 pages, Revtex, 6 eps-figures, accepted for publication in Phys. Rev.

Temperature dependence of the primary electron transfer in photosynthetic reaction centers from Rhodobacter sphaeroides

The primary electron transfer (ET) in reaction centers (RC) of Rhodobacter sphaeroides is investigated as a function of temperature with femtosecond time resolution. For temperatures from 300 to 25 K the ET to the bacteriopheophytin is characterized by a biphasic time dependence. The two time constants of τ1=3.5±0.4 ps and τ2=1.2±0.3 ps at T=300 K decrease continously with temperature to values of τ1=1.4±0.3 ps and τ2=0.3±0.15 ps at 25 K. The experimental results indicate that the ET is not thermally activated and that the same ET mechanisms are active at room and low temperatures. All observations are readily rationalized by a two-step ET model with the monomeric bacteriochlorophyll as a real electron carrier