# Tag Info

### Theoretical Computer Science vs other Sciences?

As a theoretical computer scientist I am proud of the following achievements of the field. Logicians figured out that all logical connectives can be build from a single one, paving the road for ...
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### Decidability of diophantine equations over {=, +, gcd}

($=$ is a logical symbol, hence I will not write it as part of the signature.) The satisfiability problem is decidable, as $\gcd$ has both a universal and an existential definition in terms of $|$, $+$...
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### Theoretical Computer Science vs other Sciences?

As a TCS researcher, I understand the feeling and feel it too sometimes. I think it is healthy to be able to appreciate the wonder that other sciences have to offer. We must also keep in mind that it ...
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### Entscheidungsproblem vs. Unvollständigkeitssatz (soft question)

The two words do not refer to the same thing. Hilbert's Entscheidungsproblem was the question whether there is an algorithm that decides the universal truth of first-order logical sentences, which was ...
• 4,640
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### What logic correponds via Curry-Howard to a Monad?

The two papers to look at it are Benton, Bierman and de Paiva's Computational Types from a Logical Perspective, which directly gives a proof theory for Moggi's computational lambda-calculus; and Rowan ...
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### Does the uncomputability of Kolmogorov complexity follow from Lawvere's Fixed Point Theorem?

EDIT: Adding the caveat that Roger's fixed-point theorem may not be a special case of Lawvere's. Here is a proof that may be "close"... It uses Roger's fixed-point theorem instead of Lawvere's ...
• 10.9k
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### What is the complexity of checking equivalence of two boolean formulae without NOT symbol?

Note that formulas using $\land$ and $\lor$ gates (and possibly the constants $0$ and $1$) are known as monotone. The complexity of monotone formula equivalence depends on how complex formulas are ...
• 18.2k
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### Where is the model theory in programming language theory?

The model theory of programming languages is called denotational semantics. You can google the term to find out more about it, I'll give an extreme synthesis of it. Denotational semantics is a ...
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### Where is the model theory in programming language theory?

Let me amend Damiano's answer with more specific comments. Terms of type bool are not logical statements. Expressions like ...
• 29.4k
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### Does the Law of Excluded Middle imply the Axiom K in Martin-Löf's Intensional Type Theory?

Yes, LEM implies K. See HoTT book Theorem 7.2.5, known as Hedberg's theorem, which shows that any type with decidable equality satisfies axiom $K$. If we assume excluded middle, all types have ...
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### Why/when do we ever need transfinite loop variants?

You are correct when you observe that for any particular terminating loop $L$ we may simply define the invariant "we're getting one step closer to termination". But proving that this is indeed a valid ...
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