# Tagged Questions

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### One output for input of $n$-tuples using AND, OR, NOT

Let $B$ be set of $\{0,1\}$ and $B_n$ be the set of all strings of length $n$. How many functions can be constructed from $B_n$ to $B$ using logical operators like AND, OR, NOT. Help $\rightarrow$ ...
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### Pumping Lemma & Regular Language

For each regular language L, we have an integer k such that: ...
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### The mother of all undecidable problems

It is usual to show that a problem P is undecidable by showing that the halting problem reduces to P. Is it the case that the halting problem is the mother of all undecidable problems in the sense ...
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### Names of 3 input logic gates

I've tried to look this up online, I may have used the wrong terminology. This question is about the names of logic gates with three boolean inputs, and one boolean output. This is a truth table for ...
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### predicate logic with assumption NP $\neq$ CO-NP?

Anyone could describe why: Set of All Tautology in propositional logic with assumption NP $\neq$ CO-NP is CO-NP Complete. Thanks. I ask it here before: Is the language of tautologies NP-complete? ...
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### What is the Equivalent formula of $((a\to b) \to ((a \to c) \to (c \to a)))$

Need help to solving a logic. The question is to find an equivalent to the following logic. $((a\to b) \to ((a \to c) \to (c \to a)))$ Thanks in advance for help.
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### Computable Function and Predicate Question

I See on Our Lecture note on Theory of Computation Course that: .... The basic characteristic of a computable function is that there must be a finite procedure (an algorithm) telling how to compute ...
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### Gives regular expressions which defines regular language and what does {1,2} mean

The question is give a regular expression which defines a regular language. Question: The language over {0,1} consisting of all strings which either have length less than 3 or have 0 as their third ...
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### The approximation rule implies the equality rule in systems of type assignments

I'm reading Barendregt's Lambda calculi with types (1992). In Proposition 4.1.4.1., he "proves" a lemma which shows the approximation rule implies the equality rule in typed lambda-calculi à la ...
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### Application of Combinatorics, Logic and computability theory in physical science: Tiling of Wang Tile with proportionality

The original problem of Domino Tiling and Wang Tile has great theoretical interest on computability theory... However, the great emerging problem on application of Wang Tile in material science and ...
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### Boolean algebra - cube - minimal disjunctive normal form

I have a test coming up and I would like to know how to solve these kinds of problems. This is the description: ...
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### Checking Boolean Algebra work - Simplification

I am currently working on an assignment for a CE class I am taking, and I wanted to know if I have been simplifying these equations correctly. I'm supposed to reduce them to a sum of products. 1) ...
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### Transforming Nested Fixed-Point Formulas into Infinitary Logic Formulas with Finitely many Variables

There is a definition (actually a description of how it could be defined) of a fixed-point logic formula. The formula is in inflationary fixed point logic (IFP) in this case but it could also be ...
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### Reference for problems without efficient algorithm (in polynomial time)

I'm writing paper and need your help in finding some famous (or not so famous) problems without efficient algorithm, but from logic or computer science. So far, I have: -Boolean satisfiability ...
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### Logic question- its about propositional logic and it asks for a valuation for statisfiability

I dont understand this question that comes from a past paper, so please any help is appreciated. The part that i dont understand is what does it mean (question 3) that it wants me to consider the ...
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### Is it possible that P != NP cannot be proved?

I am probably asking a stupid question but what I gather from a layman explanation of Godel's incompleteness theorem is that it is completely possible that a true statement cannot be derived from ...
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### Are axioms and rules of inference interchangeable?

There is an equivalence between cellular automata and formal systems, you can code one into the other and vice versa. But in the the cellular automata (CA) the rules of inference are fixed and are ...
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### Proving By reduction from the Halting Problem

I want to solve the following exercise in Computability and Complexity Theory: By providing a reduction from the HALTING problem to REACHABLE-CODE, prove that REACHABLE-CODE is undecidable. ...
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### Beyond Goedel incompleteness and lack of soundness/completeness of higher-order logics

As I understand that there are at least two fundamental limits of the development of the mathematics: 1) Goedel incompeleteness theorems (or more clearly Church thesis) effectively says that there ...