Undecidability of infinite post correspondence problem for instances of size 8

Abstract

The infinite Post Correspondence Problem ( ω PCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [ Theory Comput. Syst. 36 (2003) 231–245] showed that ω PCP is undecidable for domain alphabets of size 105, Halava and Harju [ RAIRO–Theor. Inf. Appl. 40 (2006) 551–557] showed that ω PCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that ω PCP is undecidable for domain alphabets of size 8.