We introduce the class of P-finite automata. These are a generalisation of weighted automata, in which the weights of transitions can depend polynomially on the length of the input word. P-finite automata can also be viewed as simple tail-recursive programs in which the arguments of recursive calls can non-linearly refer to a variable that counts the number of recursive calls. The nomenclature is motivated by the fact that over a unary alphabet P-finite automata compute so-called P-finite sequences, that is, sequences that satisfy a linear recurrence with polynomial coefficients. Our main result shows that P-finite automata can be learned in polynomial time in Angluin’s MAT exact learning model. This generalises the classical results that deterministic finite automata and weighted automata over a field are respectively polynomial-time learnable in the MAT model.
Fri 19 JanDisplayed time zone: London change
15:10 - 16:30 | Machine and Automata LearningPOPL at Kelvin Lecture Chair(s): Steven Holtzen Northeastern University | ||
15:10 20mTalk | Efficient CHAD POPL | ||
15:30 20mTalk | ReLU Hull Approximation POPL Zhongkui Ma The University of Queensland, Jiaying LI Microsoft, Guangdong Bai The University of Queensland | ||
15:50 20mTalk | On Learning Polynomial Recursive Programs POPL Alex Buna-Marginean University of Oxford, Vincent Cheval Inria Paris, Mahsa Shirmohammadi CNRS & IRIF, Paris, James Worrell University of Oxford | ||
16:10 20mTalk | Programming-by-Demonstration for Long-Horizon Robot Tasks POPL Noah Patton The University of Texas at Austin, Kia Rahmani The University of Texas at Austin, Meghana Missula The University of Texas at Austin, Joydeep Biswas The University of Texas at Austin, Işıl Dillig University of Texas at Austin | ||