Liveness-Based Garbage Collection for Lazy Languages

We consider the problem of reducing the memory required to run lazy first-order functional programs. Our approach is to analyze programs for liveness of heap-allocated data. The result of the analysis is used to preserve only live data---a subset of reachable data---during garbage collection. The result is an increase in the garbage reclaimed and a reduction in the peak memory requirement of programs. While this technique has already been shown to yield benefits for eager first-order languages, the lack of a statically determinable execution order and the presence of closures pose new challenges for lazy languages. These require changes both in the liveness analysis itself and in the design of the garbage collector. To show the effectiveness of our method, we implemented a copying collector that uses the results of the liveness analysis to preserve live objects, both evaluated (i.e., in WHNF) and closures. Our experiments confirm that for programs running with a liveness-based garbage collector, there is a significant decrease in peak memory requirements. In addition, a sizable reduction in the number of collections ensures that in spite of using a more complex garbage collector, the execution times of programs running with liveness and reachability-based collectors remain comparable

Finitary languages

The class of omega-regular languages provides a robust specification language in verification. Every omega-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens "eventually". Finitary liveness was proposed by Alur and Henzinger as a stronger formulation of liveness. It requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider automata with finitary acceptance conditions defined by finitary Buchi, parity and Streett languages. We study languages expressible by such automata: we give their topological complexity and present a regular-expression characterization. We compare the expressive power of finitary automata and give optimal algorithms for classical decisions questions. We show that the finitary languages are Sigma 2-complete; we present a complete picture of the expressive power of various classes of automata with finitary and infinitary acceptance conditions; we show that the languages defined by finitary parity automata exactly characterize the star-free fragment of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete and universality as well as language inclusion are PSPACE-complete for finitary parity and Streett automata