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Class Note for CMPSCI 601 at UMass(20)
Class Note for CMPSCI 601 at UMass(20)
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Date Created: 02/06/15
CMPSCI 601 Recall From Last Time Lecture 5 De nition A contextfree grammar CFG is a 4 tuple G V Z R S 0 V variables nonterrninals 0 Z terminals 0 R rules productions R g V X V U EV S e V 0 V Z R are all nite Pumping Lemma for Regular Sets Let D QZ6 101 be a DFA Let n Let w 6 131 st 2 n Then 3xyz E 23 st the following all hold 0 gt 0 and 0 Vk 2 maxi92 6 131 CFL Pumping Lemma Let A be a CFL Then there is a constant 72 depending only on A such that if z E A and 121 2 n then there exist strings u v w as y such that 0 z uvwacy and 0 1223 2 1 and 0 122wa g n and 0 for all k E N Maliwacky E A Prop P anbmanbm 1 n m E N is not a CFL Prop NONC FL anbncn n E N is not a CFL Any CFL satis es the conclusion of the CFL Pumping Lemma but it is not true that any nonCFL must fail to satisfy it There are other tools that can show a language to be a nonCFL These include stronger forms of the Pumping Lemma and more closure properties If A is a CFL and R a regular language then A U R must be regular Proving this however requires a different characterization of the CFL s CMPSCI 601 Pushdown Automata PDA S Lecture 5 De nition A pushdown automaton PDA is a 7 tuple P Q E l A go 20 F 0 Q nite set of states 0 Z 2 input alphabet 0 l stack alphabet 0 A g Q X 23 X l X Q X l nite set of transitions 0 go 63 Q start state 0 20 E l initial stack symbol 0 F g Q nal states PDA NFA stack Z 1062 l QOaZOgtq7X7q F7X F Theorem 51 Let A g 23 be any language Then the following are equivalent 1 A G f0r some CFG G 2 A Pf0r some PDA P 3 A is a contextfree language Proof We give only a sketch here there are detailed proofs in HMU LP and S To prove 1 implies 2 we can build a bottomup parser 0r topdown parser similar to those used in realworld compilers except that the latter are deterministic The topdown parser is a PDA that 0 begins by pushing S onto its stack 0 may pop a terminal from the stack if can at the same time read a matching input letter 0 may execute a rule A gt w by popping A and pushing 711R 0 ends by popping the when done with the input The proof that the language of any PDA is a CFL that 2 implies 1 is of less practical interest Given states 239 and 339 let Aij be the set of strings that could take the PDA from state 239 with empty stack to state 339 with empty stack We have all rules of the form Am gt Apr1n and a rule Am gt afler Whenever moves of the PDA warrant it Q CMPSCI 601 Boolean Logic Syntax Lecture 5 Boolean variables X 321322323 A boolean variable represents an atomic statement that may be either true or false There may be in nitely many of these available Boolean expressions 0 atomic 92 T top l bottom 3904V18L 067 Oz 04 gt 18 06 lt gt 7 for 0418 Boolean expressions Note that any particular expression is a nite string and thus may use only nitely many variables A literal is an atomic expression or its negation xi earl T i As you may know the choice of operators is somewhat arbitary as long as we have a complete set one that suf ces to simulate all boolean functions On HWl we argued that A V e is already a complete set The expressions form a contextfree language As we mentioned before we may cheat by omitting paren theses etc as long as the parsing is clear Even with the cheating it s not too hard to tell Whether a string is a valid expression Examples of boolean expressions 0 331 0 2 V 112 0 131 gt 132 0a gtbb gtc gta gtc CMPSCI 601 Boolean Logic Semantics Lecture 5 A boolean expression has a meaning a truth value of true or false once we know the truth values of all the individual variables A truth assignment is a function T X g X gt true false where X is the set of all variables An as signment is appropriate to an expression 0 if it assigns a value to all variables used in p The doubletumstile symbol read as models de notes the relationship between a truth assignment and an expression The statement T go read as T models cp simply says 0 is true under T If T is appropriate to p we de ne when T p is true by induction on the structure of 0 T is true and l is false for any T A variable xi is true iff T says that it is Ifcpz oz T piffb0thT aandT 8 IfltpOH8TlchiffeitherTl2a0rle or both 39Ifltpa gt8TltpunlessTozandT 8 Ifcpz ozlt gt8T ltpiffT aandT 8are both true or both false 10 De nition 52 oz and 8 are semantically equivalent 04 E 3 iff for all T appropriate to a and 8 T l 04 lt gt 3 Examples 331 E 1VL a gta E T 0a gtb E b gt a a gtb E aVb ab E av b ab E aA b aVb E bVa aVbc E abC taVbc E aVbac a E lla ll Proposition 53 Every boolean expression up is equiva lent to one in Conjunctive Normal Form CNF and to one in Disjunctl ve Normal Form DNF Proof DNF look at the truth table for p HHHHOOOOR HHOOHHOOCQ z lt gt y 0 1 O 1 1 1 O O 1 1 O O O O 1 1 O O O 1 O 1 1 1 Q syAz Q syAZ acyAZ acyAz CNF put ap in DNF Use De Morgan s law olvvok 2 e1 ak 12 De nition 54 A boolean expression 0 is satis able iff there exists T f p p is valid iff for all T appropriate to p T p Q Proposition 55 For any boolecm expression p p E UNSAT 42gt ap 6 VALID UNSAT g VALID VALID g UNSAT Proposition 56 0 p is unsatis able i cp E i p is satis able i cp E i a pisvalidi cp E T 13 CMPSCI 601 Relations With Other Models Lecture 5 A boolean expression speci es a boolean function of its variables It s natural to ask how the computation of this function ts into our other models of computation A boolean expression of length 3 can be converted into an SLP of length 86 by induction on the de nition of the expression If we already have SLP s computing 0 and 8 we can concatenate them and then with 01 more instructions compute any of the expressions oz 8 04 V 8 04 gt 8 or 04 lt gt 8 l4 Given any SLP and any of its instructions the output of the instruction is a boolean expression and thus there is some boolean expression that computes it Can we be sure that a short SLP leads to a short expression We can if the SLP is readonce meaning that each noninput variable occurs only once on the righthand side of an in struction You ll prove on HW2 that the value of 3 th in struction of a readonce SLP has an expression of length 06 It is unknown whether every polynomialsize SLP can be made readonce while keeping the size polynomial As we may prove later in the course this is equivalent to the question of whether every polynomialsize SLP can be given depth Olog n while keeping its size polynomial It is generally conjectured that it cannot 15 What about the rstorder model and boolean expres sions We can convert a V or El quanti er into a boolean ex pression using or V For example Va ltpa can be equivalently written ltpOltplltpn l where each of the ltpz39 s is one of the input bits By induction we can prove that a rstorder formula of quanti er depth d corresponds to a boolean expression in the atomic variables of length 002d Try this In this case it is known that there are polynomiallength boolean expressions that cannot be converted into rst order formulas so that the boolean expresssions are strictly more powerful We won t get to the proof of this due to Mike Sipser and three others in 1981 in this course 16 We have de ned several properties of boolean expres sions validity satis ability and their negations It is natural to ask now dif cult it is for an algorithm to take an expression as input and determine whether it is valid or satis able The method of truth tables gives us a way to answer these problems though not a very satisfactory one Given a formula in n variables there are 2 different settings of the variables 2 rows of the truth table We know how to evaluate the formula in each of these settings and thus given enough time we know how to create the entire truth table and see whether there is at least one true row or at least one false row Of course except for very small n this running time is prohibitively large Is there a better way to answer the questions We don t know and we will see that this pos sibility is tied to the major open questions of complexity theory One thing we do know is that in some circumstances we can determine the validity or satis ability of an expres sion without computing its entire truth table by giving a formal proof in some system This is our next topic 17 CMPSCI 601 The Fitch Proof System Lecture 5 If two expressions are equivalent or if one is a tautologi cal consequence of the other this fact can be established by truth tables But the 2 18 lines of the truth table are far too many to work with unless k is small We need a more ef cient method to establish tautologies BE provides a proof system called Fitch or 75 At this point in the course we are concerned with the proposi tional subset 1 of Fitch leaving out rules dealing with quanti ers 18 A Fitch proof is a sequence of expressions each one of which is justi ed in terms of previous ones There are twelve proof rules that tell us when a statement is justi ed Fitch has no axioms statements assumed to be true with out proof but we typically start with some premises and reach a conclusion that follows from those premises If from a set P of premises we can derive p we write P l ap read as P proves 90 This single turnstile symbol l is not to be confused with the double turnstile symbol l9 CMPSCI 601 7378 Propositional Proof Rules Lecture 5 These are conveniently listed on pages 5579 of BE Intro From P1 Pm derive P1 Pn Elim From P1 Pm derive a Intro From B derive P1 Pn Elim From P1 Pm if you have derived 539 sep arately from each Pi derive S e Intro If you have derived l from P derive P Elim From P derive P l Intro From P and P derive l l Elim From l derive P any P gt Intro If you have derived Q from P derive P gt Q gt Elim From P gt Q and P derive Q also called modus ponens lt gt Intro If you have derived Q from P and have derived P from Q derive P lt gt Q lt gt Elim From P lt gt Q and P derive Q 20 As you practice with the Fitch software there are two things you learn how to do You must learn when a move is legal and then when a move is a good idea In chess we call a player a beginner once they know all the moves but after a lifetime of play they will still have more to learn about how to play well The rst natural computational problem that Fitch creates is determining whether a proof is valid The software does this for your proofs and you learn to do it mentally as you look for proofs 21 A proof is valid if each step is valid and a step is valid if it follows from previous steps by a rule Eight of the rules require certain other statements to be available meaning that they are active premises or have been proved within the current scope But four of the rules Elim A In tro gt Intro and lt gt Intro require not previous state ments but previous proofs This means that Fitch proofs have a nested structure with derivations nested within other derivations We can de ne the available statements at any given point in the proof as those that are in the current derivation or any of the derivations containing the current one As computer scientists we naturally think of a stack to maintain the nesting structure At any given time we are engaged in a derivation that has certain active premises Since premises are inherited by subderivations we can keep them in a stack 22 Testing validity of a step thus involves a single pass over the current premise stack and the current derivation to see whether all the required statements or derivations for the step are there This doesn t look to be a very dif cult task We haven t yet formalized the notion of polynomial time yet in this course but once we do we can see that check ing a Fitch proof for validity takes polynomial time in the length of the proof What about the second problem of nding a reasonably short valid proof when one exists This is more dif cult of course falling into the category of arti cial in telligence There are useful heuristics but no reliable general method We ll show in the next lecture that every valid statement has a proof in Fitch But even this completeness theo rem won t tell us whether a short ie polynomiallength proof exists for every tautology This latter question is open as we ll see 23
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Venice, California resident and recovering alcoholic Chip styles himself a self-help guru but struggles to keep track of his own lies and half-truths.See more
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Nicole Kidman's children are her "greatest joys" and being a mother has given her fulfillment in her life.The 'Paperboy' actress is delighted she has experienced motherhood in so many different ways - adopting Isabella, 20, and Connor, 18, with ex-husband Tom Cruise, falling pregnant naturally with Sunday Rose, four, and using a surrogate for daughter Faith Margaret, two - and admits her personal fulfillment comes from family life.Nicole - who has her younger daughters with current spouse Keith Urban - told Grazia magazine: "I think for every woman it is different, what fulfills you in life. I never thought I'd get to experience motherhood in terms of giving birth to a child."I've experienced many different ways of how to become a mother because I have adopted children, I have birth children, I have a child through a surrogate. The greatest joys for me have come through my children."And Nicole also feels "fortunate" to be married to Keith and says she never takes any of their time together for granted.She added: "I've always wanted a partner in life, it's just who I am. I am not a loner. I've been very fortunate to find him. I don't take any day for granted in relation to a relationship - I think that's probably the greatest advice you can be given."


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London 2012 Media Watch: Victor or Victim?
China is again atop the medals table, but unseemly complaining is overshadowing this achievement
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Before I joined this forum, I was creating my own sort of Bike for the tau. I was about to send them to chapter approved, but I figured I'd show you guys, see what YOU think of them.
Sheatfish Squadron
Shasâui 35------2------3-------3---3(4)----1------2------2------8--------3+
Number/Squad:3 - 6
Weapons: Pulse Rifle
Options: The Pulse Rifle may be upgraded to Pulse Carbine at no aditional cost.
Half of the squad, rounded down, may upgrade there Pulse Rifles to Fusion Blasters or Plasma Rifles for +10 points per model.
The entire squad may buy a MarkerLight for +10 points and/or a Target lock for +5 points per model.
Each model may buy a HW multi-tracker for +10pts per model.
Fast Attack: A squad Sheatfish is a Fast Attack Choice for a Tau army.
Special Rules:
Small verhicle: Inspired by the Eldar Jetbikes, the Tau started modifying the engines of there normal verhicles, since they where to heavy for such a small verhicle. The Sheatfish being small had a great advantage on the battlefield. Therefor, Sheatfish are treated as Jetbikes instead of normal Bikes or Verhicles.
I know you said there bikes, but make sure if you do send it in that you put the line for Type: Bike or vehicle or whatever this is in there, as that's a rules issue.
is this like the tetra from forgeworld?
How do you send in rules?
Nice unit. Pretty much what I came up with in another thread about 7 pages back. I drew a pic too.
Tau Jetbikes (Tau jetbikes)
Read the special rule. it says the Sheatfish counts as a JETBIKE.Originally Posted by RSIxidor
and yes, these are just like the Tetra's from forge world. in fact, I've used the pics of tetra's to make a kind of picture of the model.
i dont think you can beat tetras in both design and fluff, theyre rules arnt too flash, and theyre engines look small, but still, i believe tau would only travel in twos at least.Originally Posted by Shas'O RenoSaurus
hey can you post those pics?
Actually, I think the little turret at the back is the Marker light, I think.
the turret at the back is a markerlight.
the tau bike should it have the same rules as eldar jetbikes? with the CTM?
CTM = Crystal Targeting Matrix???
Since when did Eldar Bikes have THAT?!?!?!?
Then get a 6" move in the assault phase in the same manner as our Crises but they don't get CTM AFAIK.


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Fat Princess
30th Jul, 2009
Fun Bits Interactive
Genre: Real Time Strategy (RTS)
Rescue your beloved princess through teamwork in this comic medieval battle royale. There's a catch, though—the other team has been feeding her magical cake, making her harder to escort back to your castle. Choose from five distinct character classes and switch at any time to best help your team. Charge head first into battle, heal teammates as the... Read More
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Create your Custom Business Card or full size CDs that share the Gospel of Jesus. Dustan Soul Adventures is a multimedia, interactive; fully Customizable Adventure program that uses Microsoft Accessibility options such as (text to speech), and a built in artificial intelligence, to compares what you believe today with what God tell us in the Bible. It will analyze your understanding of the bible, and directs you to a clear understanding of Gods Plan of Salvation for all mankind. It includes an online Bible study database that is continually updated with new study material. You can also enjoy fun and educational Bible Games like; 'I want to be a Millenniumaire', 'Wheel of Truth', Wheel of Truth in Marriage', 'The Cross-Word, Puzzles', 'Crucified for All', 'Search the Word, Puzzles'. Everyone is born, lives and then dies. It is designed to fit on a Business Card or full size CDs and it is fully Customizable. You can personalize it for your own Ministry, Business or Friends. You can change all the contact information to your personal information. This will update all the hot links, like email address, and URL to your personal Web page, as well as change the address, phone number, to your personal information. Then you can record your own personal voice greeting to what ever you like then copy your new files to a business card or full size CD and give it to your friends or business associates. Business Card CD weighs less than 1 ounce so you can include your new customized CD with a one page letter and it will only cost you the price of a first class stamp.
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General Electric Theater Caesar and Cleopatra: No description
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Cleft Lip & Palate Program
Boston Children's Hospital
This book is available for download with iBooks on your Mac or iOS device. Multi-touch books can be read with iBooks on your Mac or iOS device. Books with interactive features may work best on an iOS device. iBooks on your Mac requires OS X 10.9 or later.
The Cleft Lip and Palate Program at Boston Children's Hospital cares for more than 575 patients each year, making it one of the largest in the country. Our training, experience and commitment to innovative care with compassion has made us a national leader in the care of children and adolescents with cleft lip and palate.
Cleft lip/palate is the second most common birth defect in the United States, affecting one in 700 infants. Prenatal ultrasonography will detect cleft lip/palate in the second trimester. Detection at this stage helps parents to understand the condition and prepares them for the treatment of their child. Because the cleft involves the lip, nose and palate, it may affect hearing, speech and the teeth. A dedicated interdisciplinary team of specialists is required to treat these children. Such a team is the heart of our program. In addition to evaluation, repair and longterm management, we also give information and support to our patients and their families.
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- Free
- Category: Medical
- Published: 01 June 2012
- Publisher: Boston Children's Hospital
- Print Length: 34 Pages
- Language: English


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Detalles bibliográficos
Título: INTERNATIONAL HANDBOOK OF SCHOOL ...
Condición del libro: New
Brand New Book In Mint Condition. Shipping With Trackable Method. No APO/FPO Addresses Please. N° de ref. de la librería 9781402048050NHS
This handbook provides the most comprehensive international review of the school effectiveness and school improvement research in the twenty five years since the disciplines became prominent. The handbook contains chapters, not only from most of the key contributors to this research from the USA, the UK, Hong Kong and Europe, but also contains a number of chapters that document the progress of the field in regions of the world that are less known, including the Asian-Pacific region, Latin America, Africa and the Middle East. It contains the thoughts of not only the proponents of school effectiveness research, but those that have been critical of it. It documents the progress of the field over the past quarter century and clearly identifies the improvements in research techniques and the ability to consider context as a major feature. It provides both theoretical constructs and practical applications and case studies that are transnational and those that are local. Finally, it provides some possibilities for future research, policy and practice to guide the discipline into the next decade of change. The handbook provides a state of the art analysis of the complex issues facing schools, school systems, societies and nations that will support researchers, policy makers and practitioners in their search for ways to provide a high quality education to all students.
This book reviews of the development, implementation and practice of the disciplines of school effectiveness and school improvement. Seven main topics are addressed: History of the school effectiveness movement over the last 25 years; Changes in accountability and standards; Leadership in school effectiveness; Changes in teacher education; Impact of Diverse Populations; Education Funding and its Impact; and Best Practice Case Studies. The contributors are active in school effectiveness research worldwide.
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Librería en AbeBooks desde: 28 de noviembre de 2014
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The robot brain to rule them all: Plans for giant 'central knowledge server' to power millions of machines around the world revealed
- RoboBrain will be used in everything from home appliances to cars
- Currently downloading and processing 1 billion images, 120,000 YouTube videos and 100 million how-to documents and appliance manuals
- Internet users can correct mistakes or all to the central brain
Researchers have begun work on a giant 'robot brain' they say could be used by millions of machines around the world.
It will be a central store for everything from images to details of how to change a plug.
Hosted on a server so any robot can access it, the system is currently downloading and processing 1 billion images, 120,000 YouTube videos, and 100 million how-to documents and appliance manuals.
Scroll down for video
The information is being translated and stored in a robot-friendly format that robots will be able to draw on when they need it.
Robo Brain will process images to pick out the objects in them, and by connecting images and video with text, it will learn to recognize objects and how they are used, along with human language and behavior.
For instance, if a robot sees a coffee mug, it can learn from Robo Brain not only that it's a coffee mug, but also that liquids can be poured into or out of it, that it can be grasped by the handle, and that it must be carried upright when it is full, as opposed to when it is being carried from the dishwasher to the cupboard.
'Robo Brain is a large-scale computational system that learns from publicly available Internet resources, computer simulations, and real-life robot trials,' the researchers behind it say.
'It accumulates everything robotics into a comprehensive and interconnected knowledge base.'
Applications include prototyping for robotics research, household robots, and self-driving cars, the team say.
The information is being translated and stored in a robot-friendly format that robots will be able to draw on when they need it.
To serve as helpers in our homes, offices and factories, robots will need to understand how the world works and how the humans around them behave.
Robotics researchers have been teaching them these things one at a time: How to find your keys, pour a drink, put away dishes, and when not to interrupt two people having a conversation. This will all come in one package with Robo Brain.
'Our laptops and cell phones have access to all the information we want,' said Ashutosh Saxena, assistant professor of computer science at Cornell University
If a robot encounters a situation it hasn't seen before it can query Robo Brain in the cloud,' .
Saxena and colleagues at Cornell, Stanford and Brown universities and the University of California, Berkeley, say Robo Brain will process images to pick out the objects in them, and by connecting images and video with text, it will learn to recognize objects and how they are used, along with human language and behavior.
The system employs what computer scientists call 'structured deep learning,' where information is stored in many levels of abstraction.
An easy chair is a member of the class of chairs, and going up another level, chairs are furniture.
Robo Brain knows that chairs are something you can sit on, but that a human can also sit on a stool, a bench or the lawn.
A robot's computer brain stores what it has learned in a form mathematicians call a Markov model, which can be represented graphically as a set of points connected by lines (formally called nodes and edges).
The nodes could represent objects, actions or parts of an image, and each one is assigned a probability – how much you can vary it and still be correct. In searching for knowledge, a robot's brain makes its own chain and looks for one in the knowledge base that matches within those limits.
If a robot sees a coffee mug, it can learn from Robo Brain not only that it's a coffee mug, but also that liquids can be poured into or out of it, that it can be grasped by the handle, and that it must be carried upright when it is full, as opposed to when it is being carried from the dishwasher to the cupboard.
'The Robo Brain will look like a gigantic, branching graph with abilities for multi-dimensional queries,' said Aditya Jami, a visiting researcher art Cornell, who designed the large-scale database for the brain. Perhaps something that looks like a chart of relationships between Facebook friends, but more on the scale of the Milky Way Galaxy.
Like a human learner, Robo Brain will have teachers, thanks to crowdsourcing.
The Robo Brain website will display things the brain has learned, and visitors will be able to make additions and corrections.
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