| Links' Seminars and Public Events |   |
| 2021 | |
|---|---|
Fri 17th Sep 11:00 am 12:00 pm | Séminaire Corentin Barloy Title: Stackless Processing of Streamed Trees Abstract: Processing tree-structured data in the streaming model is a chal-lenge: capturing regular properties of streamed trees by means of astack is costly in memory, but falling back to finite-state automata drastically limits the computational power. We propose an intermediate stackless model based on register automata equipped with a single counter, used to maintain the current depth in the tree. We explore the power of this model to validate and query streamed trees. Our main result is an effective characterization of regular path queries (RPQs) that can be evaluated stacklessly—with and without registers. In particular, we confirm the conjectured characterization of tree languages defined by DTDs that are recognizable without registers, by Segoufin and Vianu (2002), in the special case of tree languages defined by means of an RPQ. Link: paperman.name/data/pub.....0.pdf  lille-Salle |
Fri 10th Sep 10:00 am 11:00 am | Séminaire de Patrick Baillot titre: Type-based complexity analysis in a parallel process calculus Abstract: Some type systems have been designed to analyse statically the time coplexity of functional languages. A natural question is whether this approach can be extended to parallel languages. We address this problem for the Pi-calculus, a paradigmatic calculus for parallel and concurrent computation. In Pi-calculus, processes communicate through channels that can carry values and channel names. We will define notions of sequential and parallel complexity for Pi-calculus, and present a type system that provides an upper bound on the time complexity of processes. This is based on joint work with Alexis Ghyselen (ESOP 2021). Based on: link.springer.com/chap.....9-3_3 |
Fri 9th Jul all day | Seminar - Antonio AL SERHALI Title: Integrating Schema-Based Cleaning into Automata Determinization Abstract : Schema-based cleaning for automata on trees or nested words was proposed recently to compute smaller deterministic automata for regular path queries on data trees. The idea is to remove all rules and states, from an automaton for the query, that are not needed to recognize any tree recognized by a given schema automaton. Unfortunately, how- ever, deterministic automata for nested words may still grow large for au- tomata for XPath queries, so that the much smaller schema-cleaned ver- sion cannot always be computed in practice. We therefore propose a new schema-based determinization algorithm that integrates schema-based cleaning directly. We prove that schema-based determinization always produces the same deterministic automaton as schema-based cleaning after standard determinization. Nevertheless, the worst-case complex- ity is considerably lower for schema-based determinization. Experiments confirm the relevance of this result in practice. |
Fri 4th Jun 10:00 am 12:30 pm | Séminaire Pierre Ohlmann Zoom link: univ-lille-fr.zoom.us/j/95419000064 Titre: Lower bound for arithmetic circuits via the Hankel matrix Abstract: We study the complexity of representing polynomials by arithmetic circuits in both the commutative and the non-commutative settings. To analyse circuits we count their number of parse trees, which describe the non-associative computations realised by the circuit. In the non-commutative setting a circuit computing a polynomial of degree d has at most 2^{O(d)} parse trees. Previous superpolynomial lower bounds were known for circuits with up to 2^{d^{1/3-ε}} parse trees, for any ε>0. Our main result is to reduce the gap by showing a superpolynomial lower bound for circuits with just a small defect in the exponent for the total number of parse trees, that is 2^{d^{1-ε}}, for any ε>0. In the commutative setting a circuit computing a polynomial of degree d has at most 2^{O(d \\log d)} parse trees. We show a superpolynomial lower bound for circuits with up to 2^{d^{1/3-ε}} parse trees, for any ε>0. When d is polylogarithmic in n, we push this further to up to 2^{d^{1-ε}} parse trees. While these two main results hold in the associative setting, our approach goes through a precise understanding of the more restricted setting where multiplication is not associative, meaning that we distinguish the polynomials (xy)z and yz). Our first and main conceptual result is a characterization result: we show that the size of the smallest circuit computing a given non-associative polynomial is exactly the rank of a matrix constructed from the polynomial and called the Hankel matrix. This result applies to the class of all circuits in both commutative and non-commutative settings, and can be seen as an extension of the seminal result of Nisan giving a similar characterization for non-commutative algebraic branching programs. Our key technical contribution is to provide generic lower bound theorems based on analyzing and decomposing the Hankel matrix, from which we derive the results mentioned above. The study of the Hankel matrix also provides a unifying approach for proving lower bounds for polynomials in the (classical) associative setting. We demonstrate this by giving alternative proofs of recent lower bounds as corollaries of our generic lower bound results. |
