Related papers: Solving Invariant Generation for Unsolvable Loops
Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection…
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. Our approach is fully automatic, meaning it does not rely on…
We introduce the concept of structured synthesis for Markov decision processes where the structure is induced from finitely many pre-specified options for a system configuration. The resulting synthesis problem is in general a nonlinear…
We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a…
It is a recent observation that entanglement classification for qubits is closely related to local $SL(2,\CC)$-invariants including the invariance under qubit permutations, which has been termed $SL^*$ invariance. In order to single out the…
We present a novel algorithm that synthesizes imperative programs for introductory programming courses. Given a set of input-output examples and a partial program, our algorithm generates a complete program that is consistent with every…
The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from…
We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…
When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer…
This paper presents a novel method for the automated synthesis of probabilistic programs. The starting point is a program sketch representing a finite family of finite-state Markov chains with related but distinct topologies, and a PCTL…
Software system can include redundant implementation elements, such as, different methods that can produce indistinguishable results. This type of redundancy is called intrinsic if it is already available in the software, although not…
We describe the Aligator.jl software package for automatically generating all polynomial invariants of the rich class of extended P-solvable loops with nested conditionals. Aligator.jl is written in the programming language Julia and is…
Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
Research on automatic software repair is concerned with the development of systems that automatically detect and repair bugs. One well-known class of bugs is the infinite loop. Every computer programmer or user has, at least once,…
A novel approach is introduced for deriving exact solutions to nonlinear systems of ordinary differential equations. This method consists of four parts. In the initial part, the examined nonlinear differential equation system is transformed…
It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In…
We consider each of the three classes of representations of cyclic groups that arise in the study of rational sphere maps. We study the possible number of terms for invariant polynomials with non-negative coefficients that are constant on…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
Consider the representations of an algebraic group G. In general, polynomial invariant functions may fail to separate orbits. The invariant subring may not be finitely generated, or the number and complexity of the generators may grow…