
Proving AlmostSure Termination of Probabilistic Programs via Incremental Pruning
The extension of classical imperative programs with realvalued random v...
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Synthesizing Probabilistic Invariants via Doob's Decomposition
When analyzing probabilistic computations, a powerful approach is to fir...
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Polynomial Invariant Generation for Nondeterministic Recursive Programs
We present a sound and complete method to generate inductive invariants ...
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OMinimal Invariants for Linear Loops
The termination analysis of linear loops plays a key role in several are...
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Probabilistic Conditional System Invariant Generation with Bayesian Inference
Invariants are a set of properties over program attributes that are expe...
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Onthefly Optimization of Parallel Computation of Symbolic Symplectic Invariants
Group invariants are used in high energy physics to define quantum field...
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Learning Invariants through Soft Unification
Human reasoning involves recognising common underlying principles across...
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Polynomial Probabilistic Invariants and the Optional Stopping Theorem
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which give rise to martingales. These polynomials are program invariants in the sense that their expected value upon termination is the same as their value at the start of the computation. In order to guarantee this we apply the Optional Stopping Theorem. Concretely, we present two approaches. The first is restricted to linear systems. In this case under positive almost sure termination there is a reduction to finding linear invariants for deterministic transition systems. Secondly, by exploiting geometric persistence properties we construct martingale invariants for general polynomial transition system. We have implemented this approach and it works on our examples.
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