Ophir Friedler

Effective post-silicon failure localization using dynamic program slicing

In post-silicon functional validation, one of the most complex and time-consuming processes is the localization of an instruction that exposes a bug detected at system level. The task is particularly difficult due to the silicons limited observability and the long time between a failures occurrence and its detection. We propose a novel method that automates the architectural localization of post-silicon test-case failures. Our proposed tool analyzes a failing test-case, while leveraging the information derived from executing the test on an Instruction Set software Simulator (ISS), to identify a set of instructions that could lead to the faulty final state. The proposed failure localization process comprises the creation of a resource dependency graph based on the execution of the test-case on the ISS, determining a program slice of instructions that influence the faulty resources, and the reduction of the set of suspicious instructions by leveraging the knowledge of the correct resources. We evaluate our proposed solution through extensive experiments. Experimental results show that, in over 97% of all cases, our method was able to narrow down the list of suspicious instructions to under 2 instructions, on average, out of over 200. In over 59% of all cases, our method correctly reduced a test-case to a single faulty instruction.

Simple Mechanisms for Agents with Complements

We study the efficiency of simple auctions in the presence of complements. Devanur et al. [2015] introduced the single-bid auction, and showed that it has a price of anarchy (PoA) of O(log m) for complement-free (i.e., subadditive) valuations. Prior to our work, no non-trivial upper bound on the PoA of single bid auctions was known for valuations exhibiting complements. We introduce a hierarchy over valuations, where levels of the hierarchy correspond to the degree of complementarity, and the PoA of the single bid auction degrades gracefully with the level of the hierarchy. This hierarchy is a refinement of the Maximum over Positive Hypergraphs (MPH) hierarchy [Feige et al. 2015], where the degree of complementarity d is captured by the maximum number of neighbours of a node in the positive hypergraph representation.We show that the price of anarchy of the single bid auction for valuations of level d of the hierarchy is O(d2 log(m/d)), where m is the number of items. We also establish an improved upper bound of O(d log m) for a subclass where every hyperedge in the positive hypergraph representation is of size at most 2 (but the degree is still d). Finally, we show that randomizing between the single bid auction and the grand bundle auction has a price of anarchy of at most O(√m) for general valuations. All of our results are derived via the smoothness framework, thus extend to coarse-correlated equilibria and to Bayes Nash equilibria.

A Unified Framework for Strong Price of Anarchy in Clustering Games

We devise a unified framework for quantifying the inefficiency of equilibria in clustering games on networks. This class of games has two properties exhibited by many real-life social and economic settings: a an agents utility is affected only by the behavior of her direct neighbors rather than that of the entire society, and b an agents utility does not depend on the actual strategies chosen by agents, but rather by whether or not other agents selected the same strategy. Our framework is sufficiently general to account for unilateral versus coordinated deviations by coalitions of different sizes, different types of relationships between agents, and different structures of strategy spaces. Many settings that have been recently studied are special cases of clustering games on networks. Using our framework: 1 We recover previous results for special cases and provide extended and improved results in a unified way. 2 We identify new settings that fall into the class of clustering games on networks and establish price of anarchy and strong price of anarchy bounds for them.

The Competition Complexity of Auctions: A Bulow-Klemperer Result for Multi-Dimensional Bidders

A seminal result of Bulow and Klemperer [1989] demonstrates the power of competition for extracting revenue: when selling a single item to n bidders whose values are drawn i.i.d. from a regular distribution, the simple welfare-maximizing VCG mechanism (in this case, a second price-auction) with one additional bidder extracts at least as much revenue in expectation as the optimal mechanism. The beauty of this theorem stems from the fact that VCG is a prior-independent mechanism, where the seller possesses no information about the distribution, and yet, by recruiting one additional bidder it performs better than any prior-dependent mechanism tailored exactly to the distribution at hand (without the additional bidder). In this work, we establish the first full Bulow-Klemperer results in multi-dimensional environments, proving that by recruiting additional bidders, the revenue of the VCG mechanism surpasses that of the optimal (possibly randomized, Bayesian incentive compatible) mechanism. For a given environment with i.i.d. bidders, we term the number of additional bidders needed to achieve this guarantee the environments competition complexity. Using the recent duality-based framework of Cai et al. [2016] for reasoning about optimal revenue, we show that the competition complexity of n bidders with additive valuations over m independent, regular items is at most n+2m-2 and at least log(m). We extend our results to bidders with additive valuations subject to downward-closed constraints, showing that these significantly more general valuations increase the competition complexity by at most an additive m-1 factor. We further improve this bound for the special case of matroid constraints, and provide additional extensions as well.

Convergence to Strong Equilibrium in Network Design Games

In a network design game [1] each agent seeks to connect two nodes in a directed network at a minimal cost. The strategies employed by each agent include all the paths that connect that agents two nodes (termed origin and destination). The paths may represent roads, internet cables, or even water pipelines. The cost of an edge is a function of the number of agents that use it. An agent pays the total cost of the edges in its path, where an edge cost is a function of the number of agents using the edge. In this work we focus on nonincreasing edge costs, where agents impose positive externalities on one another. Such settings emerge in cases where agents collectively construct a network and share the cost of the network links. Each network design game possesses a pure Nash equilibrium (PNE): an outcome that is sustainable against unilateral deviations. However, a PNE is not necessarily stable against coalitional deviations; Therefore, this is an inadequate solution concept in settings where agents are capable of coordinating their actions. The most well studied solution concept that is stable against coalitional deviations is termed strong equilibrium (SE) [2]. An SE is an outcome where no beneficial coalitional deviation (BCD) exists (i.e., a deviation in which each member of the coalition strictly decreases its cost). Epstein et al. [3] studied the existence and efficiency of SEs in non-increasing network design games. They showed that in a single-origin, any-destination (SOAD) setting (i.e., where all agents have the same origin but may have arbitrary destinations) with a seriesparallel (SP) network [3, 4], an SE is guaranteed to exist. Holzman and Monderer [4] showed that this result is tight, i.e., for any network that is not SP, there exists a non-increasing SOAD network design game that does not admit an SE. A natural question arises: Given an arbitrary outcome of an SOAD network design game with an SP network, can strategic agents converge to an SE via BCDs? and if yes, how fast? Our contribution. We start by showing that there exist BCD sequences that do not converge to an SE. We then define a class of BCDs, termed dominance based BCDs. This class is based on the notion of domination between agents. In an SOAD setting, we say that agent i is dominated by agent j if there is a path from the destination of i to the destination of j. Thus, domination is a partial order between the agents. Dominance based BCDs proceed in the following manner: Take any (full) order of the agents consistent with the partial order. Every agent i, in its turn, computes the optimal profile for itself together with all the successive agents that can intersect its path (thus reducing its cost). We show that if such a coalitional deviation reduces its cost, then every agent in the coalition benefits from the deviation as well. Therefore, this is a BCD. We show that any sequence of dominance based BCDs converges to an SE within n iterations at the most (where n is the number of agents). Moreover, we present an algorithm that efficiently computes dominance based BCDs.

99% Revenue via Enhanced Competition

A sequence of recent studies show that even in the simple setting of a single seller and a single buyer with additive, independent valuations over m items, the revenue-maximizing mechanism is prohibitively complex. This problem has been addressed using two main approaches: Approximation: the best of two simple mechanisms (sell each item separately, or sell all the items as one bundle) gives 1/6 of the optimal revenue [1]. Enhanced competition: running the simple VCG mechanism with additional m buyers extracts at least the optimal revenue in the original market [17]. Both approaches, however, suffer from severe drawbacks: On the one hand, losing 83% of the revenue is hardly acceptable in any application. On the other hand, attracting a linear number of new buyers may be prohibitive. We show that by combining the two approaches one can achieve the best of both worlds. Specifically, for any constant ε one can obtain a (1-ε) fraction of the optimal revenue by running simple mechanisms --- either selling each item separately or selling all items as a single bundle --- with substantially fewer additional buyers: logarithmic, constant, or even none in some cases.