Questions tagged [descriptive-complexity]

Classifies problems based on how hard it is to express the problem in some logical formalism.

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Decidablility of complexity properties and its relation to finite description method

We describe formal languages with their finite descriptions. For example we can describe a language simply by set-builder ( $\{ x : \phi(x)\}$) or we can describe something with its corresponding ...
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First-order iteration operator example

I am reading on https://en.wikipedia.org/wiki/FO_(complexity)#Iterating that FO[$t(n)$] consists in first-order logic with an iteration operator that iterates $t(n)$ number of times some quantifier ...
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Can we emulate logspace turing machines in FOL extended with TC bounding the number of variables?

As far as I know, Immerman showed that first-order logics extended with transitive closure (TC) captures (non deterministic) logspace (over ordered domains) [1]. That is, any database query that can ...
• 407
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Is it known whether PARTITION is NP-complete via first order reductions?

The PARTITION decision problem is defined as follows (taken from COMPUTERS AND INTRACTABILITY from Garey and Johnson): Instance: A finite set $A$ and a size $s(a) \in \mathbb{Z}^{+}$ for each $a \in A$...
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Horn formulas, existential second order logic and the Cardinality constraint

Consider this Problem $P$ as follows: $~$ Given a set $S$ and a constant $K$.. $~$Is there a subset $M$ of $S$, such that $|M| \ge K$? Of course, $P$ can be easily solved in time polynomial in $|S|$.. ...
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What is the space-complexity of a boolean first-order query?

I have the intuitition that, if we implement a (space-efficient) boolean first-order query solver, the amount of consumed memory should depend on the data size (i.e., it should not be constant). ...
• 407
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Does FOL extended with least-fixed points satisfy the Compactness Theorem?

I am aware that first-order logics (FOL) satisfies the compactness theorem. That is, if a FOL theory is insatisfiable, a finite subset of the axioms of such theory is insatisfiable too. Is it the case ...
• 407
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How to describe Deterministic Transitive Closure in FOL?

In "Finite Model Theory and Its Applications", page 152, it is said that Deterministic Transitive Closure, on ordered finite structures, captures LOGSPACE. Hence, taking into account that ...
• 407
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What does Bellantoni-Cook say about Cook-Reckov?

In implicit complexity theory they construct natural programming languages that are complete for various complexity classes. An example, while there are many others, is Bellantoni-Cook where they ...
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Descriptive complexity of 3SAT

lately I'm reading about descriptive complexity, which I find is a fascinating branch of computational complexity. I found many formulas in $\exists$$SO$ that describe problems with graphs but none ...
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1 vote
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Examples of exact computation of Kolmogorov complexity?

First question: It is known that Kolmogorov Complexity (KC) is not computable (systematically). I would like to know if there are any "real-world" examples-applications where the KC has been computed ...
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What is the motivation behind " Descriptive Complexity "?

Time and Space are two commons parameters (and also natural parameters) to measure the complexity of the problem. I am not able to understand the motivation behind defining " Descriptive Complexity". ...
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Can joins be parallelized?

Suppose we want to join two relations on a predicate. Is this in NC? I realize that a proof of it not being in NC would amount to a proof that $P\not=NC$, so I'd accept evidence of it being an open ...
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Extension of SQL capturing $\mathsf{P}$
According to Immerman, the complexity class associated with SQL queries is exactly the class of safe queries in $\mathsf{Q(FO(COUNT))}$ (first-order queries plus counting operator): SQL captures safe ...