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On the fixed parameter complexity of graph enumeration problems definable in monadic secondorder logic
, 2001
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Comparing Counting Classes for Logspace, Oneway Logspace, Logtime, and FirstOrder
 Proc. 20th Symposium on Mathematical Foundations of Computer Science, Springer Lecture Notes in Computer Science
, 1994
"... We generalize the definition of firstorder counting classes [SST92] to use !, SUCC, and + as linear orderings. It turns out that #\Pi2 [!] = #\Pi1[SUCC] = #\Pi1[+]. We introduce certain classes of logtime counting functions and show that the classes of firstorder definable counting functions are s ..."
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We generalize the definition of firstorder counting classes [SST92] to use !, SUCC, and + as linear orderings. It turns out that #\Pi2 [!] = #\Pi1[SUCC] = #\Pi1[+]. We introduce certain classes of logtime counting functions and show that the classes of firstorder definable counting functions are subclasses of the corresponding logtime counting classes. These logtime counting classes are itself subclasses of the corresponding oneway logspace counting classes. These logspace counting classes form a strict hierachy within #P: F1L` = #1L` = span1L` = #P: Using the logical characterization of #P we obtain a characterization of #P via universally branching logtime Turing machines. 1 Introduction An important open question in complexity theory is whether the two classes NL and NP are equal. Although in the case of computing partial multivalued functions nondeterministically the corresponding classes can be separated [Bur89], a solution for the class of decision problems is not in sight. ...