This is Chapter 8 of the book PAIP. It still uses pattern-match and rules to design several simple algorithms to do symbolic math simplification. I just go through the ideas in the book, and design my own program to pass all the cases in the book. The code is in https://github.com/kainwen/paip/tree/master/sym_math2/.
Continue reading千锤万凿出深山，烈火焚烧若等闲。
《石灰吟》于谦
粉骨碎身浑不怕，要留清白在人间。
This is Chapter 5 of the book PAIP. It implemented an early-day algorithm to dialog with a machine. It had the appearance of AI, but actually it was just another interpreter: programmer designs some rules at first, and then eval the user’s input. The main topic is pattern-match programming.
Pattern-match is really my favorite language feature. Erlang and many functional programming languages (Oz, ML, …) support it quite well. C language offers switch statement which can only match constant expression in each clause. Different languages may have different scopes for pattern variables.
GPS is the acronym for General Problem Solver. The book Norvig, Peter. Paradigms of artificial intelligence programming: case studies in Common LISP. Morgan Kaufmann, 1992 spent the whole Chapter 4 to show how you can program a GPS using common lisp and pointed out several “bugs” that you should pay attention to. This is a great book that I highly recommend it.
Since EOPL, I am convinced that Erlang is a very good language to implement other language or write AI paradigm program. My several projects are:
More details on Common Lisp implementation can be found in the open-source repo: https://github.com/norvig/paip-lisp.
Continue readingThe problems are from the Book Jaynes, Edwin T. Probability theory: The logic of science. Cambridge university press, 2003. Chapter 3 of the book is on the topic of Elementary sampling theory. These problems can be easily solved using the symbolic method of analytical combinatorics.
Continue readingGreenplum is MPP database. The SQL query’s planning and executing model is a distributed computing model. Greenplum introduces the concept of locus to model a path’s data distribution.
For more details, please refer to one of my talk Greenplum 查询优化器关键技术介绍.
Continue readingThis month, my most spare time has been spent on the problem Cardinality Estimate. When I finished the analysis of hyperloglog (see the blog A Tour of Understanding Hyperloglog), I just remember a recent paper of SIGMOD2019: Approximate Distinct Counts for Billions of Datasets. Its idea is to combine CountMin and Hyperloglog. Before diving into that paper, I decide to study CountMin. Another paper on cardinality estimate survey is VLDB2017’s Cardinality Estimation: An Experimental Survey mentioned a method called MinCount.
CM sketch was introduced by the paper: An Improved Data Stream Summary: The Count-Min Sketch and its Applications. I do not want to dive into that paper, but just reword the proof here (maybe in a better way).
Continue readingSee the PDF version of tutorial. It can also be downloaded here.
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Continue reading天地有正气，杂然赋流形。下则为河岳，上则为日星。於人曰浩然，沛乎塞苍冥。
皇路当清夷，含和吐明庭。时穷节乃见，一一垂丹青。在齐太史简，在晋董狐笔。
在秦张良椎，在汉苏武节。为严将军头，为嵇侍中血。为张睢阳齿，为颜常山舌。
或为辽东帽，清操厉冰雪。或为出师表，鬼神泣壮烈。或为渡江楫，慷慨吞胡羯。
或为击贼笏，逆竖头破裂。是气所磅礴，凛烈万古存。当其贯日月，生死安足论。
地维赖以立，天柱赖以尊。三纲实系命，道义为之根。嗟予遘阳九，隶也实不力。
楚囚缨其冠，传车送穷北。鼎镬甘如饴，求之不可得。阴房阗鬼火，春院闭天黑。
牛骥同一皂，鸡栖凤凰食。一朝蒙雾露，分作沟中瘠。如此再寒暑，百疠自辟易。
哀哉沮洳场，为我安乐国。岂有他缪巧，阴阳不能贼。顾此耿耿存，仰视浮云白。
悠悠我心悲，苍天曷有极。哲人日已远，典刑在夙昔。风檐展书读，古道照颜色。
《正气歌》—— 文天祥