NEEXP is Contained in MIP*

We study multiprover interactive proof systems. The power of classical multiprover interactive proof systems, in which the provers do not share entanglement, was characterized in a famous work by Babai, Fortnow, and Lund (Computational Complexity 1991), whose main result was the equality MIP = NEXP. The power of quantum multiprover interactive proof systems, in which the provers are allowed to share entanglement, has proven to be much more difficult to characterize. The best known lower-bound on MIP* is NEXP ⊆ MIP*, due to Ito and Vidick (FOCS 2012). As for upper bounds, MIP* could be as large as RE, the class of recursively enumerable languages. The main result of this work is the inclusion of NEEXP = NTIME[2^(2poly(n))] ⊆ MIP*. This is an exponential improvement over the prior lower bound and shows that proof systems with entangled provers are at least exponentially more powerful than classical provers. In our protocol the verifier delegates a classical, exponentially large MIP protocol for NEEXP to two entangled provers: the provers obtain their exponentially large questions by measuring their shared state, and use a classical PCP to certify the correctness of their exponentially-long answers. For the soundness of our protocol, it is crucial that each player should not only sample its own question correctly but also avoid performing measurements that would reveal the other player's sampled question. We ensure this by commanding the players to perform a complementary measurement, relying on the Heisenberg uncertainty principle to prevent the forbidden measurements from being performed

Preliminary multicore architecture for Introspective Computing

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 243-245).This thesis creates a framework for Introspective Computing. Introspective Computing is a computing paradigm characterized by self-aware software. Self-aware software systems use hardware mechanisms to observe an application's execution so that they may adapt execution to improve performance, reduce power consumption, or balance user-defined fitness criteria over time-varying conditions in a system environment. We dub our framework Partner Cores. The Partner Cores framework builds upon tiled multicore architectures [11, 10, 25, 9], closely coupling cores such that one may be used to observe and optimize execution in another. Partner cores incrementally collect and analyze execution traces from code cores then exploit knowledge of the hardware to optimize execution. This thesis develops a tiled architecture for the Partner Cores framework that we dub Evolve. Evolve provides a versatile substrate upon which software may coordinate core partnerships and various forms of parallelism. To do so, Evolve augments a basic tiled architecture with introspection hardware and programmable functional units. Partner Cores software systems on the Evolve hardware may follow the style of helper threading [13, 12, 6] or utilize the programmable functional units in each core to evolve application-specific coprocessor engines. This thesis work develops two Partner Cores software systems: the Dynamic Partner-Assisted Branch Predictor and the Introspective L2 Memory System (IL2). The branch predictor employs a partner core as a coprocessor engine for general dynamic branch prediction in a corresponding code core. The IL2 retasks the silicon resources of partner cores as banks of an on-chip, distributed, software L2 cache for code cores.(cont.) The IL2 employs aggressive, application-specific prefetchers for minimizing cache miss penalties and DRAM power consumption. Our results and future work show that the branch predictor is able to sustain prediction for code core branch frequencies as high as one every 7 instructions with no degradation in accuracy; updated prediction directions are available in a low minimum of 20-21 instructions. For the IL2, we develop a pixel block prefetcher for the image data structure used in a JPEG encoder benchmark and show that a 50% improvement in absolute performance is attainable.by Jonathan M. Eastep.S.M