We consider turn-based stochastic 2-player games on graphs with $$\omega $$ ω -regular winning conditions. We provide a direct symbolic algorithm for solving such games when the winning condition is formulated as a Rabin condition. For a stochastic Rabin game with k pairs over a game graph with n vertices, our algorithm runs in $$O(n^{k+2}k!)$$ O ( n k + 2 k ! ) symbolic steps, which improves the state of the art.We have implemented our symbolic algorithm, along with performance optimizations including parallellization and acceleration, in a BDD-based synthesis tool called . We demonstrate the superiority of compared to the state of the art on a set of synthetic benchmarks derived from the VLTS benchmark suite and on a control system benchmark from the literature. In our experiments, performed significantly faster with up to two orders of magnitude improvement in computation time.

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We consider fixpoint algorithms for two-player games on graphs with 𝜔-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring special case of strong fairness, which requires that any execution is strongly fair with respect to a specified set of live edges: whenever the source vertex of a live edge is visited infinitely often along a play, the edge itself is traversed infinitely often along the play as well.We show that, surprisingly, strong transition fairness retains the algorithmic characteristics of the fixpoint algorithms for 𝜔-regular games-the new algorithms can be obtained simply by replacing certain occurrences of the controllable predecessor by a new almost sure predecessor operator. For Rabin games with 𝑘 pairs, the complexity of the new algorithm is 𝑂 (𝑛 𝑘+2 𝑘!) symbolic steps, which is independent of the number of live edges in the strong transition fairness assumption. Further, we show that GR(1) specifications with strong transition fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as the usual algorithm. In contrast, strong fairness necessarily requires increasing the alternation depth depending on the number of fairness assumptions.We get symbolic algorithms for (generalized) Rabin, parity and GR(1) objectives under strong transition fairness assumptions as well as a direct symbolic algorithm for qualitative winning in stochastic 𝜔-regular games that runs in 𝑂 (𝑛 𝑘+2 𝑘!) symbolic steps, improving the state of the art. Previous approaches for handling fairness assumptions would either increase the alternation depth of the fixpoint algorithm or require an up-front automata-theoretic construction that would increase the state space, or both.Finally, we have implemented a BDD-based synthesis engine based on our algorithm. We show on a set of synthetic and real benchmarks that our algorithm is scalable, parallelizable, and outperforms previous algorithms by orders of magnitude.All proofs can be found in the appendix.

Surgical simulators provide hands-on training and learning of the necessary psychomotor skills. Automated skill evaluation of the trainee doctors based on the video of a task being performed by them is an important key step for the optimal utilization of such simulators. However, current skill evaluation techniques require accurate tracking information of the instruments which restricts their applicability to robot assisted surgeries only. In this paper, we propose a novel neural network architecture that can perform skill evaluation using video data alone (and no tracking information). Given the small dataset available for training such a system, the network trained using ℓ 2 regression loss easily overfits the training data. We propose a novel rank loss to help learn robust representation, leading to 5% improvement for skill score prediction on the benchmark JIGSAWS dataset. To demonstrate the applicability of our method on non-robotic surgeries, we contribute a new neuro-endoscopic technical skills (NETS) training dataset comprising of 100 short videos of 12 subjects. Our method achieved 27% improvement over the state of the art on the NETS dataset. Project page with source code, and data is available at nets-iitd.github.io/nets-v1.

We consider fixpoint algorithms for two-player games on graphs with $\omega$-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring special case of strong fairness, which requires that any execution is strongly fair with respect to a specified set of live edges: whenever the source vertex of a live edge is visited infinitely often along a play, the edge itself is traversed infinitely often along the play as well. We show that, surprisingly, strong transition fairness retains the algorithmic characteristics of the fixpoint algorithms for $\omega$-regular games -- the new algorithms have the same alternation depth as the classical algorithms but invoke a new type of predecessor operator. For Rabin games with $k$ pairs, the complexity of the new algorithm is $O(n^{k+2}k!)$ symbolic steps, which is independent of the number of live edges in the strong transition fairness assumption. Further, we show that GR(1) specifications with strong transition fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as the usual algorithm. In contrast, strong fairness necessarily requires increasing the alternation depth depending on the number of fairness assumptions. We get symbolic algorithms for (generalized) Rabin, parity and GR(1) objectives under strong transition fairness assumptions as well as a direct symbolic algorithm for qualitative winning in stochastic $\omega$-regular games that runs in $O(n^{k+2}k!)$ symbolic steps, improving the state of the art. Finally, we have implemented a BDD-based synthesis engine based on our algorithm. We show on a set of synthetic and real benchmarks that our algorithm is scalable, parallelizable, and outperforms previous algorithms by orders of magnitude.