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Number of pages: 186 pages Thank you very much for reading introduction to circuit complexity a uniform approach. As you may know, people have search numerous times for their chosen books like this introduction to circuit complexity a uniform approach, but end up in malicious downloads. Rather than reading a good book with a cup of coffee in the afternoon,… (More)

We explore the potentially "off-by-one" nature of the definitions of counting (#P versus #NP), difference (DP versus DNP), and unambiguous (UP versus UNP; FewP versus FewNP) classes, and make suggestions as to logical approaches in each case. We discuss the strangely differing representations that oracle and predicate models give for counting classes, and… (More)

The complexity of various problems in connection with Boolean constraints, like, for example, quantified Boolean constraint satisfaction, have been studied recently. Depending on what types of constraints may be used, the complexity of such problems varies. A very interesting observation of the recent past has been that the thus derived classification of… (More)

There has been a great eeort in giving machine independent, algebraic characterizations of complexity classes, especially of functions. Astonishingly, no satisfactory characterization of the prominent class # P has been known up to now. Here, we characterize # P as the closure of a set of simple arithmetical functions under summation and weak product.… (More)

We show that examinations of the expressive power of logical formulae enriched by Lindström quantifiers over ordered finite structures have a well-studied complexity-theoretic counterpart: the leaf language approach to define complexity classes. Model classes of formulae with Lindström quantifiers are nothing else than leaf language definable sets. Along… (More)

Building upon the known generalized-quantiier-based rst-order characterization of LOGCFL, we lay the groundwork for a deeper investigation. Speciically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantiiers. Our work extends the elaborate theory relating monoidal quantiiers to NC 1 and its subclasses. In the… (More)

In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If in contrast, the set of propositional operators is restricted, the complexity may decrease. This article systematically studies the model-checking… (More)