Abstract of Paper |

*Generalized satisfiability with \( k \) occurrences per variable: A - Study through Delta-matroid Parity*

by Victor Dalmau and Daniel Ford

**Abstract:**

In this paper we examine generalized satisfiability problems with variable occurrences. First, we show that \( 3 \) occurrences per variable suffice to make these problems as hard as their unrestricted version. Then we focus on generalized satisfiability problems with at most \( 2 \) occurrences per variable. It is known that some \( NP \)-complete generalized satisfiability problems become polynomially solvable when only \( 2 \) occurrences per variable are allowed. We identify two new families of generalized satisfiability problems, called local and binary, that are polynomially solvable when only \( 2 \) occurrences per variable are allowed. We achieve this result by means of a reduction to the \( \Delta \)-Matroid Parity Problem, which is another important theme of this work.