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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. | ||