A Characterization of Finitary Bisimulation

Following a paradigm put forward by Milner and Plotkin, a primary criterion to judge the appropriateness of denotational models for programming and specification languages is that they be in agreement with operational intuition about program behaviour. Of the "good t" criteria for such models that have beendiscussed in the literature, the most desirable one is that of full abstraction.Intuitively, a fully abstract denotational model is guaranteed to relate exactly all those programs that are operationally indistinguishable with respect to some chosen notion of observation. Because of its prominent role in process theory, bisimulation [12] has been a natural yardstick to assess the appropriateness of denotational models for several process description languages. In particular, when proving full abstractionresults for denotational semantics based on the Scott-Strachey approach for CCS-like languages, several preorders based on bisimulation have been considered; see, e.g., [6, 3, 4]. In this paper, we shall study one such bisimulationbasedpreorder whose connections with domain-theoretic models are by now well understood, viz. the prebisimulation preorder . investigated in, e.g., [6, 3]. Intuitively, p < q holds of processes p and q if p and q can simulate each other'sbehaviour, but at times the behaviour of p may be less specified than that of q. A common problem in relating denotational semantics for process descriptionlanguages, based on Scott's theory of domains or on the theory of algebraic semantics, with behavioural semantics based on bisimulation is that the chosen behavioural theory is, in general, too concrete. The reason for this phenomenon is that two programs are related by a standard denotational interpretation if, in some precise sense, they afford the same finite observations. On the other hand, bisimulation can make distinctions between the behaviours of two processesbased on infinite observations. (Cf. the seminal study [1] for a detailed analysis of this phenomenon.) To overcome this mismatch between the denotationaland the behavioural theory, all the aforementioned full abstraction results are obtained with respect to the so-called finitely observable, or finitary, part of bisimulation. The finitary bisimulation is defined on any labelled transition system thus:

Derandomizing Arthur-Merlin Games using Hitting Sets

We prove that AM (and hence Graph Nonisomorphism) is in NPif for some epsilon > 0, some language in NE intersection coNE requires nondeterministiccircuits of size 2^(epsilon n). This improves recent results of Arvindand K¨obler and of Klivans and Van Melkebeek who proved the sameconclusion, but under stronger hardness assumptions, namely, eitherthe existence of a language in NE intersection coNE which cannot be approximatedby nondeterministic circuits of size less than 2^(epsilon n) or the existenceof a language in NE intersection coNE which requires oracle circuits of size 2^(epsilon n)with oracle gates for SAT (satisfiability).The previous results on derandomizing AM were based on pseudorandomgenerators. In contrast, our approach is based on a strengtheningof Andreev, Clementi and Rolim's hitting set approach to derandomization.As a spin-off, we show that this approach is strong enoughto give an easy (if the existence of explicit dispersers can be assumedknown) proof of the following implication: For some epsilon > 0, if there isa language in E which requires nondeterministic circuits of size 2^(epsilon n),then P=BPP. This differs from Impagliazzo and Wigderson's theorem"only" by replacing deterministic circuits with nondeterministicones

Searching Constant Width Mazes Captures the AC0 Hierarchy

We show that searching a width k maze is complete for Pi_k, i.e.,for the k'th level of the AC0 hierarchy. Equivalently, st-connectivityfor width k grid graphs is complete for Pi_k. As an application, weshow that there is a data structure solving dynamic st-connectivity for constant width grid graphs with time bound O(log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools