Combinatorics on traces
On sets with efficient implicit membership tests
SIAM Journal on Computing
A uniform approach to define complexity classes
Theoretical Computer Science
Universally serializable computation
Journal of Computer and System Sciences
On the Power of Parity Polynomial Time
STACS '89 Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science
Counting Classes: Thresholds, Parity, Mods, and Fewness
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
Succinct Representation, Leaf Languages, and Projection Reductions
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Acceptance by Transformation Monoids (with an Application to Local Self Reductions)
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
The Power of Local Self-Reductions
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
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Complexity classes, which are defined via finite commutative monoids, can be considered as (very) regular counting classes. These include well-known classes like NP, coNP, ⊕P, other MOD-classes, but also the classes of finite acceptance type, and many more. In these cases, the acceptance mechanism can be defined by a regular leaf language, where acceptance really depends only on the number of occurrences of the various letters in the actual leafstring. In other words, the acceptance mechanism is given by a symmetric regular language. Generally all classes described in this way are the so called eventually periodic counting classes. In this paper we relax the symmetry condition on the regular leaf language: We allow all regular leaf languages, but we admit only machines, which on all input words will only produce symmetric leafstrings, which means all appearing leaf strings will either under all permutations belong to the acceptance language, or under all permutations not belong to the acceptance language. We give an exact characterization of all complexity classes, which can be described in this manner. It turns out that besides the classes obtained via finite commutative monoids, we also can describe promise classes like UP or MODZ2P in this way.