6 papers
Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems
William Simmons, André Platzer
Invariant sets are a key ingredient for verifying safety and other properties of cyber-physical systems that mix discrete and continuous dynamics. We adapt the elimination-theoreti…
Higher-order causal theories are models of BV-logic
Will Simmons, Aleks Kissinger
The Caus[-] construction takes a compact closed category of basic processes and yields a *-autonomous category of higher-order processes obeying certain signalling/causality constr…
Explicit polynomial bounds on prime ideals in polynomial rings over fields
William Simmons, Henry Towsner
Suppose is an ideal of a polynomial ring over a field, , and whenever with degree , then either or . When i…
Proof mining and effective bounds in differential polynomial rings
William Simmons, Henry Towsner
Using the functional interpretation from proof theory, we analyze nonconstructive proofs of several central theorems about polynomial and differential polynomial rings. We extract…
New examples (and counterexamples) of complete finite-rank differential varieties
William D. Simmons
Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective al…
On linear dependence over complete differential algebraic varieties
James Freitag, Omar Leon Sanchez, William Simmons
We extend Kolchin's results on linear dependence over projective varieties in the constants, to linear dependence over arbitrary complete differential varieties. We show that in th…