On the Expressive Power of Monadic Least Fixed Point Logic

Mathematical Foundations of Computer Science 2005

2005

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The present paper gives a classification of the expressive power of two-variable least fixed-point logics. The main results are:1. The two-variable fragment of monadic least fixed-point logic with parameters is as expressive as full monadic least fixed-point logic (on binary structures). 2. The two-variable fragment of monadic least fixed-point logic without parameters is as expressive as the two-variable fragment of binary least fixed-point logic without parameters. 3. The two-variable fragment of binary least fixed-point logic with parameters is strictly more expressive than the two-variable fragment of monadic least fixed-point logic with parameters (even on finite strings).

The Expressive Power of Two-Variable Least Fixed-Point Logics

Grohe

Kreutzer

Mathematical Foundations of Computer Science 2005

2005

Self Cite

On the Expressive Power of Monadic Least Fixed Point Logic

Automata, Languages and Programming

2004

Self Cite

Monadic least fixed point logic MLFP is a natural logic whose expressiveness lies between that of first-order logic FO and monadic second-order logic MSO. In this paper we take a closer look at the expressive power of MLFP. Our results are 1. MLFP can describe graph properties beyond any fixed level of the monadic second-order quantifier alternation hierarchy. 2. On strings with built-in addition, MLFP can describe at least all languages that belong to the linear time complexity class DLIN. 3. Settling the question whether addition-invariant MLFP ? = addition-invariant MSO on finite strings would solve open problems in complexity theory: "=" would imply that PH = PTIME whereas " =" would imply that DLIN = LINH.

On the expressive power of monadic least fixed point logic

Theoretical Computer Science

2006

Self Cite

Monadic least fixed point logic MLFP is a natural logic whose expressiveness lies between that of first-order logic FO and monadic second-order logic MSO. In this paper, we take a closer look at the expressive power of MLFP. Our results are:(1) MLFP can describe graph properties beyond any fixed level of the monadic second-order quantifier alternation hierarchy.(2) On strings with built-in addition, MLFP can describe at least all languages that belong to the linear time complexity class DLIN. (3) Settling the question whether addition-invariant MLFP ? = addition-invariant MSO on finite strings or, equivalently, settling the question whether MLFP ? = MSO on finite strings with additionwould solve open problems in complexity theory: "=" would imply that PH = PTIME whereas " =" would imply that DLIN = LINH.Apart from this we give a self-contained proof of the previously known result that MLFP is strictly less expressive than MSO on the class of finite graphs.