We present a novel static analysis technique to derive higher moments for program
variables for a large class of probabilistic loops with potentially uncountable state spaces …

Template-based synthesis, also known as sketching, is a localized approach to program
synthesis in which the programmer provides not only a specification, but also a high-level" …

We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that
hold at each location of a given affine program (ie, a program having only non-deterministic …

Automatically generating invariants, key to computer-aided analysis of probabilistic and
deterministic programs and compiler optimisation, is a challenging open problem. Whilst the …

This paper investigates the problem of reasoning about non-linear behavior of simple
numerical loops. Our approach builds on classical techniques for analyzing the behavior of …

This paper presents a program analysis method that generates program summaries
involving polynomial arithmetic. Our approach builds on prior techniques that use solvable …

This paper presents a theory of non-linear integer/real arithmetic and algorithms for
reasoning about this theory. The theory can be conceived of as an extension of linear …

This paper is the confluence of two streams of ideas in the literature on generating numerical
invariants, namely:(1) template-based methods, and (2) recurrence-based methods. A …

We present a new procedure to infer size bounds for integer programs automatically. Size
bounds are important for the deduction of bounds on the runtime complexity or in general …

We consider the termination problem for triangular weakly non-linear loops (twn-loops) over
some ring SS like ZZ, QQ, or R R. Essentially, the guard of such a loop is an arbitrary …