Unifying non-commutative arithmetic circuit lower bounds (Pierre Ohlmann)

We develop an algebraic lower bound technique in the context of non-commutative arithmetic circuits. To this end, we introduce polynomials for which the multiplication is also non-associative, and focus on their circuit complexity. We show a connection with multiplicity tree automata, leading to a general algebraic characterization. We use it to derive meta-theorems for the non-commutative case, and highlight numerous consequences in terms of lower bounds.

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Robustness of Programs Against Consistency Relaxation (Sidi Mohammed Beillahi)

Sequential Consistency (SC) and Serializability (Ser) are the classical consistency models for concurrent and distributed programs. They are the intuitive models for developers. Due to the costly synchronization required by the two models, most of existing memory models and distributed implementations of data structures do not use these two models. Instead, in order to reduce the latency and remove unnecessary synchronization, modern processors and databases adopt relaxed and weaker consistency models. However, this weakening of the consistency models implies new unexpected behaviors when running programs over the weaker models. We address in this work the problem of detecting unexpected behaviors of a program that were observed when weakening the consistency model. In particular, we check whether the two sets of executions traces of a program over the SC (resp, Ser) model and some weaker consistency model coincide or not. We characterize the set of executions traces that violate this equality and drive a decision procedure to detect these traces. In the case where there are no traces that violate this equality we refer to a program to be Robust.

A joint work with Ahmed Bouajjani and Constantin Enea