# Tagged Questions

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1answer
222 views

### Standard reference for basic model theory definitions

I am trying to give a formal presentation of the model-theoretical semantics of a language and I am a bit lost in the terminology. In particular, could somebody clarify the exact definitions of model-...
1answer
150 views

### Expressiveness of Infinitary Logic

I'm trying to put together a general picture of the expressiveness of some logics: First-Order Logics, Fixed-Point Logics, (Finite Variable) Infinitary Logics and the respected versions with Counting. ...
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58 views

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### FO-uniform AC0 with some predicate

My question is about finite model theory/descriptive complexity, so $FO(R)$ will mean "first order over finite binary words, using predicates Rs and a unary predicate P true on the position of the 1 ...
0answers
256 views

### Proof assistant formalizations of Finite Model Theory

I'm wondering if anyone knows of a formalization (even limited) of any part of finite model theory in any of the major proof assistants. (I'm most familiar with Coq, but Isabelle, Agda, etc. would ...
3answers
525 views

### What is the minimal extension of FO that captures the class of regular languages?

Context: relations between logic and automata Büchi's Theorem states that Monadic Second Order logic over strings (MSO) captures the class of regular languages. The proof actually shows that ...
1answer
250 views

### FSMs with finite memory

Consider an FSM and a finite set of variables. The FSM has the special property that each state contains a set of commands, with each command taking the form of "variable = expr(variable, ...)" e.g., ...
0answers
170 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 ...
1answer
344 views

### Database query languages for efficient queries

It seems that in popular query languages for relational databases, it is possible to create queries that will require a lot of resources to answer. In practice, database admins manage this by limiting ...
3answers
356 views

### Finding a finite model

I know that the question "does a first order formula $\phi$ have a model" is undecidable in general. Could anyone give me a link or a book which give the answer for finite models. If I have a first ...
5answers
907 views

### Ambiguity and Logic

In automata theory (finite automata, pushdown automata, ...) and in complexity, there is a notion of "ambiguity". An automaton is ambiguous if there is a word $w$ with at least two distinct accepting ...
1answer
442 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 ...
1answer
298 views

### What is the parameterized complexity of following model checking problem?

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
140 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
296 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{...
5answers
1k views

### Is there a logic without induction that captures much of P?

The Immerman-Vardi theorem states that PTIME (or P) is precisely the class of languages that can be described by a sentence of First-Order Logic together with a fixed-point operator, over the class of ...