Polynomial-time reachability for unary 2-VASS with binary-encoded configurations

Determine whether reachability in unary 2-dimensional Vector Addition Systems with States (2-VASS), when the system is encoded in unary but the initial and target configurations are encoded in binary, can be decided in polynomial time.

Background

The paper develops a polynomial-time algorithm for the special case of unary 2-dimensional Simple Linear Path Schemes (2-SLPS) with binary-encoded initial and target configurations.

The authors pose extending this algorithm beyond SLPS to general unary 2-VASS as the next step, noting that a key challenge is first obtaining such an extension for unary flat 2-VASS.