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Envy-free cake-cutting protocols procedurally divide an infinitely divisible good among a set of agents so that no agent prefers another's allocation to their own. These protocols are highly complex and difficult to prove correct. Recently, Bertram, Levinson, and Hsu introduced a language called Slice for describing and verifying cake-cutting protocols. Slice programs can be translated to formulas encoding envy-freeness, which are solved by SMT. While Slice works well on smaller protocols, it has difficulty scaling to more complex cake-cutting protocols. We improve Slice in two ways. First, we show any protocol execution in Slice can be replicated using piecewise uniform valuations. We then reduce Slice's constraint formulas to formulas within the theory of linear real arithmetic, showing that verifying envy-freeness is efficiently decidable. Second, we design and implement a linear type system which enforces that no two agents receive the same part of the good. We implement our methods and verify a range of challenging examples, including the first nontrivial four-agent protocol. 

Cache replacement policies typically use some form of statistics on past access behavior. As a common limitation, how- ever, the extent of the history being recorded is limited to either just the data in cache or, more recently, a larger but still finite-length window of accesses, because the cost of keeping a long history can easily outweigh its benefit. This paper presents a statistical method to keep track of instruction pointer-based access reuse intervals of arbitrary length and uses this information to identify the Least Ex- pected Use (LEU) blocks for replacement. LEU uses dynamic sampling supported by novel hardware that maintains a state to record arbitrarily long reuse intervals. LEU is evaluated using the Cache Replacement Championship simulator, tested on PolyBench and SPEC, and compared with five policies including a recent technique that approximates optimal caching using a fixed-length history. By maintaining statistics for an arbitrary history, LEU outperforms previous techniques for a broad range of scientific kernels, whose data reuses are longer than those in traces traditionally used in computer architecture studies.