We present a complete method for synthesizing lexicographic linear ranking functions supported by inductive linear invariants for loops with linear guards ...

Abstract. We present a complete method for synthesizing lexicographic linear ranking functions supported by inductive linear invariants for.

Linear Ranking with Reachability. Aaron R. Bradley, Zohar Manna, and Henny B ... Polyhedra-based synthesis of linear ranking functions for linear loops.

PDF | We present a complete method for synthesizing lexicographic linear ranking functions supported by inductive linear invariants for loops with.

We present a complete method for synthesizing lexicographic linear ranking functions supported by inductive linear invariants for loops with linear guards ...

The simplest (and most commonly) used test for reachability for a linear system is to check that the reachability matrix is full rank: rank⇥B AB ··· An1B⇤ = n.

2.2 Binary Reachability Analysis and Ranking Functions. Definition 1 ... Because of (10), every linear ranking function of R(x, x0) is also a ranking.

consider only linear lasso programs, linear ranking functions, and linear inductive ... Linear ranking with reachability. In. CAV, pages 491–504, 2005. 6. A. R. ...

where R+ is the reachability matrix of the system. • For discrete linear systems the reachability and controllability properties ... If A is a full rank matrix, ...

Ranking functions for linear-constraint loops. (POPL 2013). ▻ lexicographic linear ranking functions. Bradley, Manna, Sipma. Linear ranking with reachability.