Date/Time : 17 Apr 2019 17:00
Venue : S17 #04-06 SR1
Speaker : Liu Tianyu,

Date/Time:17 Apr 2019 17:00 Venue: S17 #04-06 SR1 Speaker: Liu Tianyu Arithmetic algorithm of surreal numbers The surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers. A surreal number is sometimes defined as a function from an initial segment of the ordinals into the set $(+,-)$, usually leads to an infinite sign sequence. It can also be expressed uniquely in a normal form, as $\sum_{i<\alpha} \omega^{a_i}r_i$. In this talk I will present some algorithms for addition, multiplication and division on the real field. Besides, we will cover the normal form and sign sequence of surreal numbers, which will be crucial for arithmetic algorithm of surreal numbers of length $>\omega$. Add to calendar: 

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Date/Time : 10 Apr 2019 17:00
Venue : S17 #04-06 SR1
Speaker : Gao Ziyuan, National University of Singapore

Date/Time:10 Apr 2019 17:00 Venue: S17 #04-06 SR1 Speaker: Gao Ziyuan, National University of Singapore Finitely distinguishable erasing pattern languages with bounded variable frequency A pattern is a nonempty string made up of symbols from two disjoint sets, an alphabet $\Sigma$ of constant symbols and a countably infinite set $X$ of variables. The erasing pattern language $L(\pi)$ generated by a pattern $\pi$ is the set of all words over $\Sigma$ obtained by replacing all the variables of $\pi$ with arbitrary words over $\Sigma$, with the proviso that identical variables be replaced with the same string. In particular, patterns allow for repetitions of variable substrings, a feature known as backreferencing in programming languages. A distinguishing set for any pattern $\pi$ w.r.t. a class $\Pi$ of patterns containing $\pi$ is a set $D$ of words over $\Sigma$ that distinguishes $\pi$ from every other pattern $\tau$ in $\Pi$ with $L(\tau) \neq L(\pi)$ (i.e., $D \cap L(\pi) \neq D \cap L(\tau)$ whenever $L(\tau) \neq L(\pi)$). Two basic types of counting problems will be discussed: first, given any pattern $\pi$ belonging to a class $\Pi$ of patterns, does $\pi$ have a finite distinguishing set w.r.t. $\Pi$; second, what is the minimum size of a distinguishing set for $\pi$ w.r.t. $\Pi$? The latter quantity gives a measure of the information complexity of $\pi$ w.r.t. $\Pi$, and it is known as the (classical) teaching dimension of $\pi$ w.r.t. $\Pi$ in computational learning theory. We also consider the problem of determining, for any given strict partial order $\prec$ on $\Pi$ (up to equivalence of patterns) and any pattern $\pi$ belonging to $\Pi$, the minimum size of a distinguishing set for $\pi$ w.r.t. the subclass of all $\tau$ in $\Pi$ such that $\tau \not\prec \pi$; this quantity is known as the preference-based teaching dimension of $\pi$ w.r.t. $(\Pi,\prec)$. We study how the classical and preference-based teaching dimensions of patterns w.r.t. various “naturally” defined classes of patterns and strict partial orders depend on the alphabet size and the maximum number of variable repetitions in any single pattern belonging to the class. Add to calendar: 

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