# Questions tagged [induction]

Questions about mathematical induction and inductive proofs.

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### Failing to solve a recurrence by induction

My question is strongly related to the one asked here: How do I show T(n) = 2T(n-1) + k is O(2^n)? $$T(n)=2T(n-1)+1$$ Going with the steps, I reached the point where: $$c*2^{n}\geq c*2^{n}+1$$ which ...
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### How can I prove the correctness of this exponentiation algorithm using induction?

I have the following algorithm. How could I prove it using induction that for every $n\ge 0$, Exp(n)${}= 2 ^ n$? ...
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### Is Inductive Logic Programming approach applicable to general theories (not just sets of Horn clauses)?

Inductive Logic Programming (https://en.wikipedia.org/wiki/Inductive_logic_programming) find hypothesis theory H for background theory B and set of examples E. ILP algorithms and implementations ...
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### How to show a function is primitive recursive by induction?

I know, loosely speaking, if we can define a function $f$ in term of \begin{align} &f(0,\vec{x})=g(\vec{x})\\ &f(n+1,\vec{x})=h(f(n),n,\vec{x}) \end{align} where functions $g,h$ are primitive ...
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### Proving that a property is k-inductive with an SMT solver (parametric resettable counter)

I'm following the slides at https://homepage.cs.uiowa.edu/~tinelli/talks/FT-11.pdf where Tinelli explains how k-induction works in the context of SMT based model checking. A parametric and resettable ...
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### Proving a DFA recognizes a language using induction

The following DFA recognizes the language containing either the substring $101$ or $010$. I need to prove this by using induction. So far, I have managed to split each state up was follows: q0: ...
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### Proof that this sorting algorithm sorts the input [duplicate]

I'm given this "sorting" algorithm and now I'm supposed to prove, that if given an array of integers of length $n$, sort(A,0,n-1) will sort it. ...
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### Recursive definition for the length of a string?

I found a couple of answers online but I don't quite understand why the answer is right: The length of a string is: If a string has no characters, then its length is 0. Otherwise, the length of the ...
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### Is my proof of my greedy algorithm to find subsequence correct?

Credit to KleinBerg and Taros Book Some of your friends have gotten into the burgeoning field of time-series data mining, in which one looks for patterns in sequences of events that occur over time. ...
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### Iterative Fibonacci algorithm correctness proof, finding loop invariants

The algorithm take in an integer $n$ and outputs the $n$th number in the Fibonacci sequence ($F_n$). The sequence starts with $F_0$. I am trying to prove the correctness assuming valid input: ...