On 1-inkdot alternating Turing machines with small space

Abstract

This paper investigates the accepting powers of nondeterministic and alternating 1-inkdot Turing machines using small space. Let NTM (ATM, UTM) denote a nondeterministic Turing machine (alternating Turing machine, alternating Turing machine with only universal states). For each Xϵ{N, A, U}, let STRONG-XSPACE[ L( n)] (STRONG-XSPACE ∗[ L( n)]) denote the class of languages accepted by strongly L( n) space-bounded XTMs (1-inkdot XTMs), and let WEAK-XSPACE[ L( n)] (WEAK-XSPACE ∗[ L( n)]) denote the class of languages accepted by weakly L( n) space-bounded XTMs (1-inkdot XTMs). We show that 1. (1) STRONG-ASPACE∗[log log n ] - WEAK-ASPACE[o(log n )]≠∅, 2. (2) STRONG-USPACE∗[log log n ] - WEAK-USPACE[o(log n )]≠∅, 3. (3) STRONG-ASPACE∗[log log n ] - WEAK-NSPACE∗[o(log n )]≠∅, and 4. (4) STRONG-ASPACE∗[log log n ] - WEAK-USPACE∗[o(log n )]≠∅.