# 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.

634 questions
Filter by
Sorted by
Tagged with
23 views

### NP-hardness proof of an optimization problem with real values and real input in the decision problem

Question - Let's suppose we have an optimization problem $\mathcal{P}$ with a real-valued measure function and the decision version of the optimization problem $\mathcal{P}_D$ (please see definitions ...
62 views

### NP-hardness proof of an optimization problem with real values and rational input in the decision problem

I'm studying complexity theory and I have the below question regarding $NP$-hardness proofs of optimization problems with real values. Any reference is much appreciated. For the question, take the ...
53 views

### How to prove that the problem $\text{"If$L$is a context-free language, then, is$\overline{L}$also context-free?"}$ is undecidable?

Lately I came across a problem: $\text{"If$L$is a context-free language, then, is$\overline{L}$also context-free?"}$ And I need to comment on its decidability. Now I know that context free ...
100 views

### Invariant vs Assertion vs lemma

I am reading Distributed Algorithms by Nancy Lynch. I have come across lemmas, assertions and invariants, but I do not understand the difference between them. I think lemma means an intermediate ...
40 views

### Mutual Friends in a Network?

I always seem to have trouble finding a formal way to analyze this (be through proofs or whatever). The problem statement is as such: If A and B are friends, and B and C are friends, then A and C are ...
26 views

### M does not accept [M] | 'Correction' of proof possible?

The language $D=\{[M]|M([M])=0\}$ is not decidable because of the following argument: Suppose there was a $TM \space M_D$ that decides $D$. Then if we gave $M_D \space [M]$, there would be two ...
38 views

### How can I use induction for proving termination of a string rewriting system?

If we have a string rewriting system within the alphabet $\{X,Y\}^*$ and the rule $XY\to YX$. How can we prove by induction that on every string input the system terminates?
50 views

### Proof that for every $k > 1$, there exists a language $A_k \subseteq \{0, 1\}^*$ s.t. a DFA accepting $A_k$ has $k$ states but no less

I am trying to prove that for every $k > 1$, there exists a language $A_k \subseteq \{0, 1\}^*$ such that a DFA accepting $A_k$ has $k$ states but no less. I thought about proving this in two ways: ...
46 views

### How to prove NP-hardness of a Hamiltonian Path problem by reducing longest-path problem?

I know how to prove longest-path problem by reducing Hamiltonian Path problem. Here I want to prove NP-hardness of a Hamiltonion Path problem by reducing longest-path problem. (pretend we know longest-...
34 views

### Please help me understand this proof of the undecidability of "Do two halting Turing machines accept the same language?"

Do two halting Turing machines accept the same language? Proof that it is undecidable(credit to another user on this website: "Tom van der Zanden"): Let M be an arbitrary Turing machine. Let ...
23 views

### Proving that $f(n) \not\in O(n)$ given that $f(n) \in \Theta(n^2)$ and the formal definitions of Big-Oh and Theta

So far I've understood that because of the definition of $\Theta$, we have $c_1n^2 \le f(n) \le c_2n^2$. I'm not sure how to proceed from there.
81 views

220 views

### Can every sentence of first-order logic be converted into an equisatisfiable equation in Boolean algebra?

There may be some theoretical literature, unknown to me, that addresses this question. If possible, I would like a practical approach to this problem. My attempt involves the use of an equational ...
39 views

### why is behaviour of simpl differ so much after a commutative operation and how to inspect simpl?

In Coq, while trying to prove a lemma mult_n_Sm for mult_comm, I have this equation in a proof: ...