Find a finite automaton that recognizes the language $$L=\{w\in\{a,b\}^*\mid\text{$w$ has an odd quantity of $a$ and an even quantity of $b$}\}.$$ Indicate whether the automata is deterministic or not.     I tried to find a regular expression for $L$: $$(a(aa)^*+(bb)^*)^*$$ but then I realized that $\lambda\notin L$ since there is not odd quantity of $a$, so my final regex is $$(a(aa)^*+(bb)^*)^+$$ I am not able to find an automata for this language. I tried with:    but if we call $z=a(aa)^*+(bb)^*$ then I am not able to graph $z^+$.  How can we get the automata?
I'm having trouble understanding the wording of one of my homework questions. Since this question appears early in the chapter, I have a feeling that I'm misinterpreting it.  Give a finite automaton that that accepts the following language: The language over $\{a, b\}$ of any even number of $a$'s and any odd number of $b$'s.   I'm having trouble with the usage of "and". Is it asking for an FA that accepts any string that is either an even number of $a$'s or an odd number of $b$'s, e.g. $aa$, $bbb$, $aaaa$, etc, but not accept strings like $aabbb$, $abbab$.   Or, is it asking for an FA that accepts any string that contains an even number of $a$'s or an odd number of $b$'s, e.g. $aabbb$, $ababb$, etc.   The first case is relatively simple, but I've been struggling with the second. I haven't even managed to convince myself that it is a regular language (because I haven't been able to come up with a regular expression that matches it).   My questions: Which interpretation seems most likely. Is the second case a regular language, if so, give a regular expression that recognizes it.
Why do I get different values for $x from the snippets below?  #!/bin/bash  x=1 echo fred &gt; junk ; while read var ; do x=55 ; done &lt; junk echo x=$x  #    x=55 .. I'd expect this result  x=1 cat junk | while read var ; do x=55 ; done echo x=$x  #    x=1 .. but why?  x=1 echo fred | while read var ; do x=55 ; done echo x=$x  #    x=1  .. but why? Scoring when two triple word squares are covered in one play The word QUAGMIRE is on the board vertically, with the Q on the top row, second column. The next player creates SQUEEZED horizontally, landing the S on the triple word square in the top row, first column, and remaining UEEZED landing to the right of the existing Q, ending with the D on the triple word square in the eighth column. Since two triple word squares are covered in this one placement, how would it be scored?  Letters:   S: 1 Q: 10 U: 1 E: 1 x 2 (double letter) E: 1 Z: 10 E: 1 D: 1   27 Total for letters. Do you then multiply by 3 for the first triple word square, and then multiply that result by 3?  27 X 3 = 81, 81 X 3 = 243  Bonus for all 7 tiles placed:  243 + 50 = 293 Extracting raster values at points using Open Source GIS? How to create custom config section in app.config? Installing node with apt-get or downloading the Linux Binaries (.tar.gz) Bounty not awarded automatically — bug? Cannot create an array of LinkedLists in Java...? Should a button become lighter or darker on hover? We're having a discussion in the office about whether a button should become lighter or darker when a user hovers over it.   Here are some examples from the field:  Apple "Buy Now" button (Second is hover, third is depressed) -     Twitter Bootstrap -    (Unselected)   (Hover)  Github homepage - github.com      The button on FogBugz homepage goes from yellow to slightly lighter yellow. The buttons on Optimizely and Visual Website Optimizer hardly change.  Amazon's "Buy Now" button doesn't do anything when you hover over it (besides change to a pointer cursor). The colored buttons in Google's new interface (see Gmail or Calendar) go slightly darker when you hover over them.  Finally here is our button:    Should your button become lighter or darker when you hover over it? What else should you consider? Does anyone have data on whether the hover effect matters for conversions? Deleting your own closed questions fails silently on the mobile site There is some sort of delay for deletion of your own closed questions (2 days, I think) for non-mods. Now, when you try deleting a closed question on the desktop site, it nicely tells you "please wait xyz to allow for possible reopening" (in a box similar to the "please consider adding a comment explaining why you downvoted" thingy).  On mobile, it just reloads the page—there is no indicator that deletion is not allowed.  Either completely disable the delete button on mobile for closed questions, or give it a popup as well. Not letting the user know what's wrong is confusing. How do you judge the quality of a journal? How to automate entry of external column data in BCS? I have a document library, Resumes, that has a large number of resumes in it. There is a regular column on that library, called EmployeeID, that is already populated.  I have an external content type ( ECT ) that is mapped to a table that lists EmployeeID and several other columns of information. I added this ECT to the library as an External Column.    I am looking for a good way to automatically go through all items in the document library, and copy the value from the "regular" EmployeeID column into the External EmployeeID column and have it update the other columns from the ECT. Any techniques are useful (PowerShell, Object Model, Workflow?) When we have tried this in the past with workflows the setting of the External Column did not report failure, but didn't actually trigger a lookup of the other data and the value didn't seem to actually get saved.  [Update] I have been working on this and am getting closer. I am using PowerShell to access the list and set the external column ID field to the value I want it to be.  The problem is that it doesn't seem to be triggering a lookup of the external data when that field is set.  my "list" (a document library) has a few normal fields and a set of external columns mapped to an ECT "EmplData".  When you use the GUI to add or edit the properties of an item, it works. When I use PowerShell to do the following:  $spList = $spWeb.Lists["Resumes"] $spListItem = $spList.GetItemById(1) $spListItem["EmplData_ID"] = "00300"    $spListItem.Update()   Sometime the external ID field gets updated when I the refresh the web page, other times it says "(blank)". In all cases it does not load in the other fields.  Is there some Update method that updates the rest of the elements?  I gather from research that these are called "secondary fields", is the method to update the secondary fields based on the external item ID available in PowerShell cmdlets someplace?  [Update] I am finding that if I use:  $spListItem["EmplData"] = "000300"   instead of $spListItem["EmplData_ID"] = "00300" it gets around the problem of the column showing "(blank)".   I still need to figure how to make it update the other external columns (also known as "secondary columns" I think) When conducting multiple regression, when should you center your predictor variables & when should you standardize them? In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized.  (Standardizing consists in subtracting the mean and dividing by the standard deviation.)  In which other cases do I need to standardize my data?  Are there cases in which I should only center my data (i.e., without dividing by standard deviation)? How do I get the linksys WUSB6300 wireless adapter to work on linux Inbox chops messages in the middle of an HTML character reference The messages in the inbox get chopped if they too long, and the chop can occur in the middle of an HTML character reference as can be seen in this screenshot:    The character being chopped is [ and it appears inside a code snippet, in case it makes a difference. C++ single template specialisation with multiple template parameters Movie/TV series with a scene of spiky, black goo growing out of a lab container? There was a scene from a sci-fi horror video, not animated, don't know if it's a movie or TV series, where there was this black goo in a glass container and some scientists were looking at it under a microscope.   The pitch black goo grew and grew so fast, eventually breaking out of the inner box and the scientists that were inside the "inner lab" were begging to get out but the scientists outside that inner lab refused to open the door. The black goo was spiky (had spikes).  It's not any of the "Alien" movies, "The Blob", "Life", or "The Thing". It's not vintage. It was made after 1990, I'm pretty sure. How to Disable new terms (free tagging) with Taxonomies? Adding values to a C# array Can't pair apple wireless keyboard Keyboard: Apple Wireless Keyboard (model number MC184LL/B)  System: Macbook Pro Early 2011 running OS X 10.8  The keyboard gets detected and when I try to pair it, the system asks to enter some numbers through the keyboard.   However when I press the key (on the wireless keyboard) nothing happens, the only key that seems to work (i.e. to move to the next key in the code) is 0. I can also press enter to confirm but it always fails (since the only code I can enter is 0000...0).   I've also tried pairing from the bluetooth preference and changing the passcode option. However this won't work either.   Any ideas? The keyboard was paired with another MacBook Pro (I don't have access to it anymore). Is there any method to 'reset' the keyboard to factory settings? In Java is there a way to check the condition:  "Does this single character appear at all in string x"  without using a loop?