CSCI 5832 Natural Language Processing Lecture 3 Jim Martin 1 23 07 CSCI 5832 Spring 2006 1 Today 1 23 Review FSA Determinism and Non Determinism Combining FSA English Morphology 1 23 07 CSCI 5832 Spring 2006 2 1 Review Regular expressions are just a compact textual representation of FSAs Recognition is the process of determining if a string input is in the language defined by some machine Recognition is straightforward with deterministic machines 1 23 07 CSCI 5832 Spring 2006 3 D Recognize 1 23 07 CSCI 5832 Spring 2006 4 2 Three Views Three equivalent formal ways to look at what we re up to not including tables Regular Expressions Finite State Automata 1 23 07 Regular Languages CSCI 5832 Spring 2006 5 Regular Languages More on these in a couple of weeks S A A 1 23 07 b a a A a A CSCI 5832 Spring 2006 6 3 Non Determinism 1 23 07 CSCI 5832 Spring 2006 7 Non Determinism cont Yet another technique Epsilon transitions Key point these transitions do not examine or advance the tape during recognition 1 23 07 CSCI 5832 Spring 2006 8 4 Equivalence Non deterministic machines can be converted to deterministic ones with a fairly simple construction That means that they have the same power nondeterministic machines are not more powerful than deterministic ones in terms of the languages they can accept It also means that one way to do recognition with a non deterministic machine is to turn it into a deterministic one 1 23 07 CSCI 5832 Spring 2006 9 Non Deterministic Recognition In a ND FSA there exists at least one path through the machine for a string that is in the language defined by the machine But not all paths directed through the machine for an accept string lead to an accept state No paths through the machine lead to an accept state for a string not in the language 1 23 07 CSCI 5832 Spring 2006 10 5 Non Deterministic Recognition So success in a non deterministic recognition occurs when a path is found through the machine that ends in an accept Failure occurs when all of the possible paths lead to failure 1 23 07 CSCI 5832 Spring 2006 11 Example b q0 1 23 07 a q1 a a q2 q2 CSCI 5832 Spring 2006 q3 q4 12 6 Example 1 23 07 CSCI 5832 Spring 2006 13 Example 1 23 07 CSCI 5832 Spring 2006 14 7 Example 1 23 07 CSCI 5832 Spring 2006 15 Example 1 23 07 CSCI 5832 Spring 2006 16 8 Example 1 23 07 CSCI 5832 Spring 2006 17 Example 1 23 07 CSCI 5832 Spring 2006 18 9 Example 1 23 07 CSCI 5832 Spring 2006 19 Example 1 23 07 CSCI 5832 Spring 2006 20 10 Key Points States in the search space are pairings of tape positions and states in the machine By keeping track of as yet unexplored states a recognizer can systematically explore all the paths through the machine given an input 1 23 07 CSCI 5832 Spring 2006 21 ND Recognize 1 23 07 CSCI 5832 Spring 2006 22 11 Infinite Search If you re not careful such searches can go into an infinite loop How 1 23 07 CSCI 5832 Spring 2006 23 Why Bother Non determinism doesn t get us more formal power and it causes headaches so why bother More natural understandable solutions 1 23 07 CSCI 5832 Spring 2006 24 12 Compositional Machines Formal languages are just sets of strings Therefore we can talk about various set operations intersection union concatenation This turns out to be a useful exercise 1 23 07 CSCI 5832 Spring 2006 25 Union 1 23 07 CSCI 5832 Spring 2006 26 13 Concatenation 1 23 07 CSCI 5832 Spring 2006 27 Negation Construct a machine M2 to accept all strings not accepted by machine M1 and reject all the strings accepted by M1 Invert all the accept and not accept states in M1 Does that work for non deterministic machines 1 23 07 CSCI 5832 Spring 2006 28 14 Intersection Accept a string that is in both of two specified languages An indirect construction A B A or B 1 23 07 CSCI 5832 Spring 2006 29 Motivation Let s have a meeting on Thursday Jan 26th Writing an FSA to recognize English date expressions is not terribly hard Except for the part about rejecting invalid dates Write two FSAs one for the form of the dates and one for the calendar arithmetic part Intersect the two machines 1 23 07 CSCI 5832 Spring 2006 30 15 Administration Homework questions Anything else 1 23 07 CSCI 5832 Spring 2006 31 Assignment 1 Strings are an easy and not very good way to represent texts Normally we want lists of sentences that consist of lists of tokens that ultimately may point to strings representing words lexemes Lists are central to Python and will make your life easy if you let them 1 23 07 CSCI 5832 Spring 2006 32 16 Transition Finite state methods are particularly useful in dealing with a lexicon Lots of devices some with limited memory need access to big lists of words So we ll switch to talking about some facts about words and then come back to computational methods 1 23 07 CSCI 5832 Spring 2006 33 English Morphology Morphology is the study of the ways that words are built up from smaller meaningful units called morphemes We can usefully divide morphemes into two classes Stems The core meaning bearing units Affixes Bits and pieces that adhere to stems to change their meanings and grammatical functions 1 23 07 CSCI 5832 Spring 2006 34 17 English Morphology We can also divide morphology up into two broad classes Inflectional Derivational 1 23 07 CSCI 5832 Spring 2006 35 Word Classes By word class we have in mind familiar notions like noun and verb We ll go into the gory details in Ch 5 Right now we re concerned with word classes because the way that stems and affixes combine is based to a large degree on the word class of the stem 1 23 07 CSCI 5832 Spring 2006 36 18 Inflectional Morphology Inflectional morphology concerns the combination of stems and affixes where the resulting word Has the same word class as the original Serves a grammatical semantic purpose that is Different from the original But nevertheless transparently related to the original 1 23 07 CSCI 5832 Spring 2006 37 Nouns and Verbs English Nouns are simple Markers for plural and possessive Verbs are only slightly more complex Markers appropriate to the tense of the verb 1 23 07 CSCI 5832 Spring 2006 38 19 Regulars and Irregulars Ok so it gets a little complicated by the fact that some words misbehave refuse to follow the rules Mouse mice goose geese ox oxen Go went fly flew The terms regular and irregular will be used to refer to words that follow the rules and those that don t 1 23 07 CSCI 5832 Spring 2006 39 Regular and Irregular Verbs Regulars Walk walks walking walked walked Irregulars …
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