Palindrome language and Finite Automata Machines I'm a grad student in math. I'm unaware of available literature in theoretical computer science, so require suggestions for books. Here are the two topics I'm interested in exploring.

1) A complete treatment of palindrome language with reference to finite automata, particularly interested in how a probabilistic finite automate would recognize palindrome language. 

2) A thorough treatment of context-sensitive languages. Introductory books don't discuss it in details as it is perhaps not a topic to be studied in a first course. 

it appears that introductory books have rather sketchy discussions of the topics, mostly end of chapter problems. Any suggestion is greatly appreciated.
Regarding probabilistic (and quantum) automata, you may start by digging this survey: https://arxiv.org/abs/1507.01988

For very recent results on quantum automata, you may check two recent works by Zachary Remscrim: https://eccc.weizmann.ac.il/author/659/

Palindrome is an (exclusive) stochastic language, but a probabilistic machine requires log-space to recognize it with bounded error. Two-way quantum automata recognizes palindrome language with bounded-error in super-polynomial time.