# Questions tagged [descriptive-complexity]

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

47 questions
Filter by
Sorted by
Tagged with
115 views

### Descriptive Complexity characterzation of BPP

We know of descriptive complexity characterizations of classes such as P, and NP, which use First Order logic, and operators. Does BPP have a characterization under descriptive complexity, too(any ...
120 views

### Reductions in Descriptive Complexity

Reducing one problem to another are well known in various settings, such as many-one, randomized, truth-table, logspace or a whole slew of other reductions. Descriptive complexity can alternately ...
55 views

### Inexpressibility of Second order

In finite model theory, Ehrenfeucht-Fraïssé games gives us tools to prove inexpressibility results for FOL. Pebble games do the same for infinitary logic with finitely many variables. Do we have such ...
171 views

### P and Descriptive Complexity

In the Complexity Zoo, it says  that, in descriptive complexity, $P$ can be defined by three different kind of formulae, $FO(LFP)$ which is also $FO(n^{O(1)})$, and also as $SO(HORN)$. However, ...
94 views

### Proof of SAT is complete for NP via first-order reductions

So I have been reading this: https://people.cs.umass.edu/~immerman/book/ch7.pdf I do not understand the proof of theorem 7.16, which says that SAT is complete for NP via first-order reductions. My ...
124 views

### Descriptive model theory classification of Counting hierarchy

Descriptive model theory uses logic to characterize complexity classes How to model Counting Hierarchy PSPACE in descriptive model theory?
317 views

188 views

193 views

### Logic capturing automorphism-invariant $\mathsf{AC^0}$ properties

Q1. Is there a logic that is computable in polynomial-time which contains all order-invariant properties computable in smaller classes like $\mathsf{AC^0}$ (or $\mathsf{TC^0}$)? Motivation As you ...
162 views

### Using MSOL for solving BIDS problem

From "Linear Time Solvable Optimization Problems on Graphs of Bounded Clique Width" (B. Courcelle et al) we know that any problem that can be written on MSOL (Monadic Second Order Logic) has a linear ...
1k views

### Why do relational databases work at all, given the theoretical exponential complexity of answer finding (in the size of the query)?

It seems to be known that to find an answer to a query $Q$ over a relational database $D$, one needs time $|D|^{|Q|}$, and one cannot get rid of the exponent $|Q|$. As $D$ can be very large, we ...
875 views

### What is First-Order Rewritable (and FO-Query)?

I just wonder what FO Rewritable is, put an example to make it clearer for me. Also, I heard that a language that is FO Rewritable is very good, in what sense? It is said as follow: A class C of ...
431 views

### MSOL optimization problems on graphs of bounded cliquewidth, with cardinality predicates

CMSOL is Counting Monadic Second Order Logic, i.e. a logic of graphs where the domain is the set of vertices and edges, there are predicates for vertex-vertex adjacency and edge-vertex incidence, ...
305 views

Input: Graph $G$ and formula $\varphi_1(\vec x),\varphi_2(\vec x)$ Parameter: $tw(G)+|\varphi_1|+|\varphi_2|$ Problem: Decide if $|\varphi_1(G)|=|\varphi_2(G)|$ where $tw(G)$ is the treewidth of $... 3answers 145 views ### Searching for matching queries Suppose you have a large set of queries (could be in SQL form, but conceivably the same problem exists for search engine query strings or Lucene expressions, etc...) stored and you want to know which ... 1answer 382 views ### Could a descriptive complexity version of Rice's theorem be used to separate AC0 and PSPACE? In this question, it was mentioned that there are descriptive complexity versions of Rice's theorem. I found a proof of the following theorem: Given a complexity class C, nontrivial properties of ... 1answer 153 views ### Is testing two SO-Horn queries for equivalence decidable? It follows from Rice's theorem that you cannot determine whether or not two Turing machines decide the same language. My question is: Does this also apply in descriptive complexity settings, ... 2answers 742 views ### Are there descriptive complexity representations of quantum complexity classes? The title more or less says it all, but I guess I could add a bit of background and some specific examples I'm interested in. Descriptive complexity theorists, such as Immerman and Fagin, have ... 1answer 332 views ### SAT in finite model theory without order It is well known in finite model theory that without an order on the input, the expressivity is very limited. For example it is known that$FO(<,\textit{PFP})$is equal to PSPACE, and$FO(\textit{...
Let $\pi \colon \{0,1\}^* \to \{0,1\}^*$ be a permutation. Note that while $\pi$ acts on an infinite domain, its description might be finite. By description, I mean a program that describes $\pi$'s ...