# Time and Space Complexity of Inside-Out Macro Languages

P.R.J. Asveld

Research output: Book/ReportReportOther research output

## Abstract

Starting form Fischer's IO Standard Form Theorem we show that for each inside-out (or IO-) macro language $L$ there exists a $\lambda$-free IO macro grammar with the following property: for each $x$ in $L$ there is a derivation of $x$ of length at most linear in the length of $x$. Then we construct a nondeterministic log-space bounded auxiliary pushdown automaton which accepts $L$ in polynomial time. Therefore the IO-macro languages are (many-one) log-space reducible to the context-free languages. Consequently, the membership problem for IO-macro languages can be solved deterministically in polynomial time and in space $(\log n)^2$.
Original language English Amsterdam Mathematical Centre, Deptartment of Computer Science 13 Published - 1980

### Publication series

Name CWI report Mathematical Centre, Deptartment of Computer Science 141/80 0376-4028

## Keywords

• Inside-out macro grammar
• Nondeterministic log-space bounded auxiliary pushdown automaton
• Complexity of membership problem
• (Many-one) log-space reducibility
• HMI-SLT: Speech and Language Technology

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