Decidability and complexity for reversible 2-head language classes

Investigate decidability problems, computational complexity, and descriptional complexity for the language classes 2revLIN (reversible deterministic 2-head automata), 2rev1LIN (1-limited reversible 2-head automata), and 2CrevLIN (complete reversible 2-head automata), determining which questions are decidable and quantifying recognition and representation complexity within these models.

Background

Beyond structural inclusion results, the paper highlights that foundational questions about algorithmic decidability and complexity for the new reversible two-head classes remain unanswered. These include, at a high level, whether standard decision problems for these automata are decidable, what computational resources are required to recognize their languages, and how succinctly languages can be represented within these models compared to others.

Resolving these questions will clarify the practical and theoretical viability of reversible two-head automata, connect them to established complexity theory, and quantify descriptional trade-offs relative to deterministic two-head automata and linear grammars.