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regular_expressions_for_automata_with_parallel_inputs [2009/04/28 20:24] vkuncak |
regular_expressions_for_automata_with_parallel_inputs [2009/04/28 20:26] vkuncak |
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| ====== Regular Expressions and Automata with Parallel Inputs ====== | ====== Regular Expressions and Automata with Parallel Inputs ====== | ||
| - | Given an alphabet $\Sigma = \{0,1\}$, we consider a larger (but still finite) alphabet $\Sigma^n$ for some $n$. Keep in mind that $(a_1,\ldots,a_n) \in \Sigma_n$ is just one symbol; we often write it as | + | Given an alphabet $\Sigma$, we consider a larger (but still finite) alphabet $\Sigma^n$ for some $n$. Keep in mind that $(a_1,\ldots,a_n) \in \Sigma_n$ is just one symbol; we often write it as |
| \[\left( | \[\left( | ||
| \begin{array}{l} | \begin{array}{l} | ||
| Line 16: | Line 16: | ||
| on such alphabets. | on such alphabets. | ||
| - | Example: $\Sigma = \{0,1\}$. Let $n=3$. | + | ====== Using Propositional Formulas to Denote Finite Sets of Symbols ====== |
| + | |||
| + | Suppose $\Sigma = \{0,1\}$. | ||
| + | |||
| + | Let $n=3$. | ||
| $\Sigma^3 = \{ (0,0,0),(0,0,1),\ldots,(1,1,1) \}$. | $\Sigma^3 = \{ (0,0,0),(0,0,1),\ldots,(1,1,1) \}$. | ||
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| \right) | \right) | ||
| \] | \] | ||
| - | The bitwise and relation is given by | + | The bitwise **and** relation, shown above, is given by |
| \[ | \[ | ||
| [z \leftrightarrow (x \land y)]^* | [z \leftrightarrow (x \land y)]^* | ||