PPT- Three New Algorithms for Regular Language Enumeration

Erkki Makinen University of Tempere Tempere Finland Margareta Ackerman University of Waterloo Waterloo ON What kind of words does this NFA accepts 0 1 1 1 0 1 0 A B C D. ca shallitgracelanduwaterlooca Abstract The crosssection enumeration problem is to list all words of length in a regular language in lexicographical order The enumeration problem is to list the 64257rst words in according to radix order We present an Generating Subsets You might recall the knapsack problem or subset sum problem which may require us to enumerate through all subsets until we find one that solves the problem. We can generate subsets CS 4705. Some . slides adapted . from Hirschberg, Dorr/. Monz. , . Jurafsky. Some simple problems: . How much is Google worth?. How much is the Empire State Building worth?. How much is Columbia University worth?. Definitions. Equivalence to Finite Automata. 2. RE. ’. s: Introduction. Regular expressions. describe languages by an algebra.. They describe exactly the regular languages.. If E is a regular expression, then L(E) is the language it defines.. Formal definition of a regular expression.. Languages associated with regular expressions.. Introduction regular grammars. . Regular language and homomorphism. . The Chomsky Hierarchy . Regular Expression. Reading: Chapter 3. 2. Regular Expressions vs. Finite Automata. Offers a declarative way to express the pattern of any string we want to accept . E.g., . 01*+ 10*. Automata => more machine-like . < input: string , output: [accept/reject] >. Definition. Scanning identifies live hosts and running services . Enumeration probes the identified services more fully for known weaknesses . Enumeration is more intrusive, using active connections and directed queries. Erkki. . Makinen. University of . Tempere. . Tempere. , Finland. Margareta Ackerman. University of Waterloo. Waterloo, ON. What kind of words does this NFA accepts?. 0. 1. 1. 1. 0. 1. 0. A. B. C. D. Regular Languages. Regular languages are the languages which are accepted by a Finite Automaton.. Not all languages are regular. Non-Regular Languages. L. 0. = {. a. k. b. k. : k≤0} = . {ε}. is a regular language. Fall 2017. http://cseweb.ucsd.edu/classes/fa17/cse105-a/. Today's learning goals . Sipser Ch 1.2, 1.3. Decide whether or not a string is described by a given regular expression. Design a regular expression to describe a given language. (review). Some special IP addresses. localhost 127.0.0.1 (loopback address). Internal networks. Class A 10.0.0.0. Class B 172.16.0.0 to 172.31.0.0. Class C 192.168.0.0 to 192.168.255.0. Machines behind a firewall can use these internal IP numbers to communicate among them. . Chapter 3 REGULAR LANGUAGES AND REGULAR GRAMMARS Learning Objectives At the conclusion of the chapter, the student will be able to: Identify the language associated with a regular expression Find a regular expression to describe a given language Learning . Objectives. At the conclusion of the chapter, the student will be able to:. State the closure properties applicable to regular languages. Prove that regular languages are closed under union, concatenation, star-closure, complementation, and intersection. 2. Regular Expressions vs. Finite Automata. Offers a declarative way to express the pattern of any string we want to accept . E.g., . 01*+ 10*. Automata => more machine-like . < input: string , output: [accept/reject] >.