computer-science

Is it impossible to know if two functions are equivalent? For example, a compiler writer wants to determine if two functions that the developer has written perform the same operation, what methods can he use to figure that one out? Or can what can we do to find out that two TMs are identical? Is there a way to normalize the machines? Edit: If the general case is undecidable, how much information do you need to have before you can correctly say that two functions are equivalent? Given an arbitrary function, f , we define a function f' which returns 1 on input n if f halts on input n . Now, for

Could someone provide a good description of what a Lambda is? We have a tag for them and they're on the secrets of C# question, but I have yet to find a good definition and explanation of what they are in the first place. Closures, lambdas, and anonymous functions are not necessarily the same thing. An anonymous function is any function that doesn't have (or, at least, need) its own name. A closure is a function that can access variables that were in its lexical scope when it was declared, even after they have fallen out of scope. Anonymous functions do not necessarily have to be closures, but

I am new to Matlab and trying to figure out how can I deal with overflow and underflow arithmetic when the answer is actually within the range. For example: x = 2e+160 x = x*x (which returns inf, an overflow) x = sqrt(x) (which is in the range) any help is appreciated. I am not a Matlab user so take that in mind. The main problem behind this is first to detect overflow/underflows That is sometimes hard because they appear also in other cases when the computation does not return zero or inf . For example during numerical integration overflow/underflows can cause the result to be wrong but still

I need to write a regular expression that can detect a string that contains only the characters x,y, and z, but where the characters are different from their neighbors. Here is an example xyzxzyz = Pass xyxyxyx = Pass xxyzxz = Fail (repeated x) zzzxxzz = Fail (adjacent characters are repeated) I thought that this would work ((x|y|z)?)*, but it does not seem to work. Any suggestions? EDIT Please note, I am looking for an answer that does not allow for look ahead or look behind operations. The only operations allowed are alternation, concatenation, grouping, and closure Usually for this type of

For general-purpose sorting, the answer appears to be no, as quick sort, merge sort and heap sort tend to perform better in the average- and worst-case scenarios. However, insertion sort appears to excel at incremental sorting, that is, adding elements to a list one at a time over an extended period of time while keeping the list sorted, especially if the insertion sort is implemented as a linked list (O(log n) average case vs. O(n)). However, a heap seems to be able to perform just (or nearly) as well for incremental sorting (adding or removing a single element from a heap has a worst-case

Whenever people ask about the halting problem as it pertains to programming, people respond with "If you just add one loop, you've got the halting program and therefore you can't automate task " Makes sense. If your program has an infinite loop, then when your program is running, you have no way of knowing whether the program is still crunching input, or if it is just looping infinitely. But some of this seems counter intuitive. What if I was writing a halting problem solver, which takes source code as its input. rascher@localhost$ ./haltingSolver source.c If my code (source.c) looks like this

What does the term referential transparency mean? I've heard it described as "it means you can replace equals with equals" but this seems like an inadequate explanation. Uday Reddy The term "referential transparency" comes from analytical philosophy , the branch of philosophy that analyzes natural language constructs, statements and arguments based on the methods of logic and mathematics. In other words, it is the closest subject outside computer science to what we call programming language semantics . The philosopher Willard Quine was responsible for initiating the concept of referential