TheoComp
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Fichier Détails
| Cartes-fiches | 23 |
|---|---|
| Langue | Deutsch |
| Catégorie | Informatique |
| Niveau | École primaire |
| Crée / Actualisé | 12.06.2025 / 14.06.2025 |
| Lien de web |
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Any infinite language is regular
Any finite language is regular
Any infinite language is not regular
The language \(\emptyset\) is regular
The language \(\emptyset\) is context-free
The language \(\{\epsilon\}\) is not regular
Any context-free language is regular
Any not-context free language is infinite
Any regular language is finite
Any context-free language is infinite
If a language L is regular, then L* is regular
If a Language L is regular, then \(\overline{L}\) is regular
Define P
Decision problems solvable by a deterministic Turing machine in polynomial time.
Define NP
Decision problems whose yes-instances can be verified in polynomial time by a deterministic Turing machine (equivalently, solvable in polynomial time by a nondeterministic Turing machine).
Define co-P
Decision problems whose no-instances are solvable by a deterministic Turing machine in polynomial time (i.e., complements of problems in P).
Note: Since P is closed under complement, co-P = P.
Define co-NP
Decision problems whose no-instances can be verified in polynomial time (complements of problems in NP).
Define NP-complete
Problems in NP that are at least as hard as every problem in NP:
Membership: They themselves lie in NP.
Hardness: Every NP problem reduces to them via a polynomial-time many-to-one reduction.
If any NP-complete problem is solved in polynomial time, P = NP.
Define NP-hard
Problems at least as hard as the hardest problems in NP (every NP problem reduces to them), but not required to be in NP; they may be decision, optimization, or even non-decidable problems.
Palindromes are...
The language \(\emptyset\) is...
Equivalence of two TMs is...
Define co-P again:
co-P is the class of decision problems whose complements are solvable by a deterministic Turing machine in polynomial time:
We know that 2-COLOR decision problem belongs to P. However, is the brute force algorithm for this problem bounded by a polynomial?
A straightforward “brute-force’’ procedure tries every possible colouring of the n vertices with two colours and checks whether any of them respects all m edges. That requires examining 2ⁿ assignments, each verified in O(n + m) time, for a worst-case running time Θ(2ⁿ · (n + m)), which is exponential—not polynomial—in the input size.
The fact that 2-COLOR is in P comes from a different algorithm (e.g. a single BFS/DFS per connected component to test bipartiteness) that runs in O(n + m) time. Thus membership in P guarantees the existence of a polynomial-time algorithm, but the naïve brute-force method is not one of them.
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