Paul Higham

Closed-Face Integrality and Exact Conditional Termination for Cone-Monotone Integer Equality Relations

This paper gives an exact characterization of conditional termination for a class of nondeterministic homogeneous integer equality relations defined by Bλ = Aλ′ over nonnegative integer coefficient vectors. Under pointedness of the source cone, nonzero source generators and cone-...

Closed-Face Integrality and Exact Conditional Termination for Cone-Monotone Integer Equality Relations

This paper gives an exact characterization of conditional termination for a class of nondeterministic homogeneous integer equality relations defined by Bλ = Aλ′ over nonnegative integer coefficient vectors. Under pointedness of the source cone, nonzero source generators and cone-...

Non-negative Positionality in Regular Abstract Numeration Systems: Balance-Loop Normal Forms and Infinite Integer Viability

This paper develops an exact normal form for the nonnegative positionality problem in regular abstract numeration systems. A companion paper showed that, after an effectively computable finite preperiod and periodic phase lift, affine positionality is governed by a finite homogen...

Intrinsic Affine Positionality in Ordered Regular Languages: Fixed-Width and Genealogical Rank

This paper develops an intrinsic affine theory of positional rank in prefix-closed, right-prolongable ordered regular languages. It characterizes when fixed-width lexicographic ranks and more general unit-spaced graded ranks admit a normalized scalar positional representation. Po...