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sav08:deciding_a_language_of_sets_and_relations [2009/05/14 12:05]
vkuncak
sav08:deciding_a_language_of_sets_and_relations [2015/04/21 17:30] (current)
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Consider a simple language of sets: Consider a simple language of sets:

-$+\begin{equation*} \begin{array}{l} \begin{array}{l} S ::= V \mid S \cup S \mid S \cap S \mid S \setminus S \mid \mathbf{U} \mid \emptyset \\ S ::= V \mid S \cup S \mid S \cap S \mid S \setminus S \mid \mathbf{U} \mid \emptyset \\ A ::= (S = S) \mid (S \subseteq S) \mid card(S){=}c \mid card(S) \leq c \mid card(S) \geq c \\ A ::= (S = S) \mid (S \subseteq S) \mid card(S){=}c \mid card(S) \leq c \mid card(S) \geq c \\ - F ::= F \lor F \mid F \land F \mid \lnot F \\+ F ::= F \lor F \mid F \land F \mid \lnot F \mid A \\ c ::= 0 \mid 1 \mid 2 \mid ... c ::= 0 \mid 1 \mid 2 \mid ... \end{array} \end{array} -$+\end{equation*}

We show that this language is decidable by reduction to universal class. We show that this language is decidable by reduction to universal class. 