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Questions tagged [proof-techniques]

Questions about general methods and techniques for proving multiple theorems. When asking about the proof of a single statement, use tags relating to what the proof is about instead.

694 questions
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Does a proof using the well-ordering principle need a base case?

For proofs by well-ordering principle the general template is to consider the negation of some predicate $P(n)$. Then assume the set of all elements that fulfill $\lnot P(n)$, i.e. $\qquad N = \{ n \mid \lnot P(n) \}$ has a smallest element…
Abdul Rahman
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Proving a value is the result of the execution of an algorithm

Assuming an algorithm $A$ known to both Alice and Bob. Alice runs the algorithm and gets a result $R$. How can Alice prove to Bob that $R$ is the result of the execution of $A$ and not some random value (without having Bob run the algorithm…
BGR
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what is routine induction?

I read a paper which mentioned routine induction many times. But when I google it, there are nothing showed up. I think routine induction means the induction on the structure, analyzing possible cases in proofs. am I right? Just to make sure, I am…
alim
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How do we know that Icosoku always has solutions?

This is a continuation of a question I asked here. The puzzle Icosoku is now described by Wikipedia as: "The puzzle frame is a blue plastic icosahedron, and the pieces are 20 white equilateral-triangular snap-in tiles with black dots and 12 yellow…
Craig Feinstein
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how real example projects apply formal proof techniques

Given that there are examples of formal proofs used to formally verify real-world software applications, I would like to know what these people and teams actually do to create these formal proofs. That is, the kind of code they write and/or the…
Lance
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The floor function

How do I prove or disprove the following statements: $$(a) ∀n ∈ \mathbb N, ∃k ∈ \mathbb N, ∀x ∈ \mathbb R , \lfloor nx \rfloor − n \lfloor x \rfloor ≤ k$$ and $$ (b)\exists k \in \mathbb N, \forall n \in \mathbb N, \forall x \in \mathbb R, \lfloor…
HKT
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Not understand exchanging argument proof for optimal prefix code

I am currently reading the Algorithm Design textbook by Kleinberg and Tardos and I am having difficulty understanding a proof using an exchange argument Statement: A binary tree corresponding to the optimal prefix code is full Proof: This is easy to…
user2635911
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Linear Bound Automaton Power

Please tell me is their deterministic linear bound automaton same power as non-deterministic linear bound automaton to recognize any language?
Ulfat Imdad
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Prove that an $n$-length string has $2^n$ i18n-style abbreviations

An i18n-style abbreviation is one in which multiple letters are shortened to that number of letters. E.g., "internationalization" -> "i18n" ("nternationalizatio" is substituted with its length 18). Other abbreviations include "in17n", "i17on",…
Steven
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What do we conclude from diagonalization principle?

I understand $R_{fa}$ etc. I understand why the diagonals are higlighted. I understand D={a,d,f}. But I don't understand what is the conclusion we derive from this?
ladhee
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Is it common to prove that some code is the simplest way to achieve something?

I have a simple program which achieves a certain functionality. I’m interested to know if it can be proven that the steps in the program are the theoretically simplest way to achieve those results. Is it an established practice in computer science…
Julius Hamilton
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Proving Minimum Sequence Disjoint Set

Prove that 9 is the minimum number of calls to make-set, union-set, find-set such that a disjoint set union using weight (number of nodes) by path compression and disjoint set union using rank (upper bound on height) such that the trees produced by…
Ukatoon
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Is there a proof that "undetectable" malware cannot be written?

In Fred Cohen's paper "Computer Viruses - Theory and Experiments", he proves that for the general case, classifying malware is an undecidable problem. I was wondering whether there might be a similarly well-known proof that an undetectable malware…
kansas_bulldog382
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Isn't ZKP is a reduction to a hard problem, rather than true zero knowledge?

Take for example "Hamiltonian cycle for a large graph". The proof works by starting with a graph G that contains a hamiltonian cycle, then constructing an isomorphic graph H, and then either showing the mapping between the graphs G and H or…
TNB
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How to prove that a stack is equivalent to a queue with reversed inputs

Say I push the values 1,2,3,4 onto a stack. Then popping them, they will come back in the order 4,3,2,1. If I push the values 1,2,3,4 onto a queue then removing from a queue results in 1,2,3,4. However if I push them onto the queue in reverse order,…
sashang
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