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visibly_pushdown_languages [2007/05/31 12:01] vkuncak |
visibly_pushdown_languages [2007/06/05 11:20] vkuncak |
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| Stack always contains $\bot$ as the bottom element. A visibly pushdown automaton never pushes or pops $\bot$. | Stack always contains $\bot$ as the bottom element. A visibly pushdown automaton never pushes or pops $\bot$. | ||
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| + | ===== Every context-free language is a 'projection' of some visibly pushdown language ===== | ||
| ===== Closure properties ===== | ===== Closure properties ===== | ||
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| Solution: not just a set of states, but a summary of relation from initial to final states of 'procedure'. Then update directly the effect of a procedure call on each state. | Solution: not just a set of states, but a summary of relation from initial to final states of 'procedure'. Then update directly the effect of a procedure call on each state. | ||
| - | Note: you never store original symbols on the stack. | + | Note: you never store original symbols on the stack (but we store the call input symbol). |
| ===== MSOL over strings with matching relation ===== | ===== MSOL over strings with matching relation ===== | ||
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| Thanks to closure properties. | Thanks to closure properties. | ||
| - | ===== Strack trees ===== | + | |
| + | ===== Stack trees ===== | ||
| We can associate //injectively// trees with words over pushdown alphabet, then visibly pushdown languages correspond to regular trees. | We can associate //injectively// trees with words over pushdown alphabet, then visibly pushdown languages correspond to regular trees. | ||