Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | Next revision Both sides next revision | ||
sav08:remarks_on_ws1s_complexity [2009/04/29 10:56] vkuncak |
sav08:remarks_on_ws1s_complexity [2010/11/23 19:22] hossein |
||
---|---|---|---|
Line 1: | Line 1: | ||
====== Remarks on WS1S Complexity ====== | ====== Remarks on WS1S Complexity ====== | ||
+ | |||
===== Complexity of One Algorithm ===== | ===== Complexity of One Algorithm ===== | ||
The construction in [[Using Automata to Decide WS1S]] determinizes automaton whenever it needs to perform negation. Moreover, existential quantifier forces the automaton to be non-deterministic. Therefore, with every alternation between $\exists$ and $\forall$ we obtain an exponential blowup. For formula with n alternations we have $2^{2^{\ldots 2}}$ complexity with a stack of exponentials of height $n$. Is there a better algorithm? | The construction in [[Using Automata to Decide WS1S]] determinizes automaton whenever it needs to perform negation. Moreover, existential quantifier forces the automaton to be non-deterministic. Therefore, with every alternation between $\exists$ and $\forall$ we obtain an exponential blowup. For formula with n alternations we have $2^{2^{\ldots 2}}$ complexity with a stack of exponentials of height $n$. Is there a better algorithm? | ||
+ | |||
+ | ===== Reference ===== | ||
+ | A. R. Meyer: [[http://publications.csail.mit.edu/lcs/pubs/pdf/MIT-LCS-TM-038.pdf|Weak monadic second order theory of successor is not elementary recursive]], Preliminary Report, 1973. | ||
===== Lower Bound ===== | ===== Lower Bound ===== |