Questions tagged [finite-model-theory]

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DFA and RE find out the language. Please can you explain?

Find the regular expression describing following languages over alphabet {0, 1}*. ...
86 views

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 $|S|$.. ...
82 views

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 ...
22 views

Let M a finite state transducer define as : $M=<X,Y,S,\delta,\lambda>$ What we mean by quasi-linear finite automata?
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Defining $a^n b^{n^2}$ with one existential SO binary relation

Is it possible to define the language: $$L = \{ a^n \; b^{n^2} \}$$ using an existential second order sentence over strings (ordered structures with unary predicates $U_a(x), U_b(x)$) using only ...
69 views

Datalog Program Equivalence with Fixed Universe Size

It is well known that to compute equivalence of two Datalog programs (or equivalently of two first order formulas with the least fixed point operator) wrt all possible inputs and universes, is ...
57 views

LTL and alternation

Apparently, model checking LTL on Kripke structures is PSPACE-complete (see this question). Usually, when something in finite model theory is PSPACE-hard, there is a simple proof using the APTIME ...
258 views

Datalog Self Interpretation

According to https://link.springer.com/article/10.1007%2Fs001530050135 (Logics that define their own semantics, Imhof 1999) the logic FO[LFP] can define its own semantics, though the proof (of ...