No Efficient Disjunction or Conjunction of Switch-Lists

TL;DR

The paper demonstrates that combining switch-lists through disjunction or conjunction can cause exponential increases in representation size, highlighting limitations in their efficiency for logical operations.

Contribution

It proves that disjunction and conjunction of switch-lists can lead to exponential blow-up, revealing fundamental limitations in their use for logical representations.

Findings

Disjunction of switch-lists can exponentially increase size.

Negation of switch-lists does not increase size.

Conjunction of switch-lists also causes exponential blow-up.

Abstract

It is shown that disjunction of two switch-lists can blow up the representation size exponentially. Since switch-lists can be negated without any increase in size, this shows that conjunction of switch-lists also leads to an exponential blow-up in general.