Hao Wu, Jiyu Zhu, Amir Kafshdar Goharshady, Jie An, Bican Xia, Naijun Zhan
In this paper, we address the complexity barrier inherent in Fourier-Motzkin elimination (FME) and cylindrical algebraic decomposition (CAD) when eliminating a block of (existential) quantifiers. To mitigate this, we propose exploiting structural sparsity in the variable dependency graph of quantified formulas. Utilizing tools from parameterized algorithms, we investigate the role of treewidth, a parameter that measures the graph's tree-likeness, in the process of quantifier elimination. A novel dynamic programming framework, structured over a tree decomposition of the dependency graph, is developed for applying FME and CAD, and is also extensible to general quantifier elimination procedures. Crucially, we prove that when the treewidth is a constant, the framework achieves a significant exponential complexity improvement for both FME and CAD, reducing the worst-case complexity bound from doubly exponential to single exponential. Preliminary experiments on sparse linear real arithmetic (LRA) and nonlinear real arithmetic (NRA) benchmarks confirm that our algorithm outperforms the existing popular heuristic-based approaches on instances exhibiting low treewidth.
Streaming speech-to-speech translation requires timely decisions about when partial input is sufficient for accurate translation. We present S3-S2ST, a model that learns to translate and speak from semantically aligned streaming supervision. By converting utterance-level speech pairs into incremental training examples, we teach a learned policy when to commit translations. Its adjustable threshold controls the quality--latency tradeoff on a fixed 640\,ms input grid. S3-S2ST delivers competitive English--Chinese translation on FLEURS and leads the evaluated streaming systems in translation quality on the internal 9-pair test set. On RealSI, adapting the threshold to buffered speech further improves quality over a low fixed threshold with little change in first-audio latency. We plan to release the model and code.