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Questions about methods and techniques to prove correctness of programs.

2 votes
Accepted

What's the meaning of the $\top$ symbol in a Hoare triple?

The symbol $\top$, known as top, stands for "True". There is also a symbol $\bot$, known as bottom, which stands for "False". Top is always true, and bottom is always false. In your case, having a pre …
Yuval Filmus's user avatar
3 votes
Accepted

Evaluation of reverse Polish notation

How do you define the semantics of RPN? Ignoring the print commands, I would imagine a recursive definition that, given a sequence of operations, tells you what the state of the stack is like. From th …
Yuval Filmus's user avatar
2 votes
Accepted

Complex property of sparse horner polynomials by induction

You need to use induction on some complexity measure $\mu(x,y)$ (on some well-ordered domain) which has the following property: When running the addition procedure on $x,y$, all recursive calls ar …
Yuval Filmus's user avatar
1 vote

How do you check if two algorithms return the same result for any input?

It is impossible to devise an algorithm that does prove this equality in general. Hint: reduction from the Halting problem.
Yuval Filmus's user avatar
5 votes

Imperfection in randomness in VLC shuffle playlist - why?

This is just speculation, but perhaps what VLC is attempting is to simulate... perfect randomness. That is, each song is picked uniformly at random, independently of previous songs. According to the c …
Yuval Filmus's user avatar