Abstract We present the first machine learning approach to termination analysis of probabilistic programs. Ranking supermartingales (RSMs) prove that programs halt, in expectation, within a finite number steps. While previously RSMs were directly synthesised from source code, our method learns them sampled execution traces. introduce neural ranking supermartingale : we let network fit an RSM ov...

Data envelopment analysis (DEA) is one of the most efficient tools for efficiency measurement which can be employed as a benchmarking method with multiple inputs and outputs. However, DEA does not provide any suggestions for improving efficient units, nor does it provide any benchmark or reference point for these efficient units. Impracticability of these benchmarks under environmental conditio...

 Many Limit Theorems, Convergence Theorems and Characterization Theorems in Probability and Statistics, in particular those related to normal distribution , are based on the assumption of independence of two or more random variables. However, the full power of independence is not used in the proofs of these Theorems, since it is the distribution of summation of the random variables whic...

The SHUNYATA program constructs proof methods by analyzing proofs of simple theorems in mathematical theories such as group theory and uses these methods to form prooh of new theorems in the same or in other theories. Such methods are capable of generating proo& of theorems whose complexity represents the state of the art in automated theorem proving. They are composed of elementary functions s...