Certifying Confluence of Almost Orthogonal CTRSs via Exact Tree Automata Completion

Suzuki et al. showed that properly oriented, right-stable, orthogonal, and oriented conditional term rewrite systems with extra variables in right-hand sides are confluent. We present our Isabelle/HOL formalization of this result, including two generalizations. On the one hand, we relax proper orientedness and orthogonality to extended proper orientedness and almost orthogonality modulo infeasibility, as suggested by Suzuki et al. On the other hand, we further loosen the requirements of the latter, enabling more powerful methods for proving infeasibility of conditional critical pairs. Furthermore, we formalized a construction by Jacquemard that employs exact tree automata completion for non-reachability analysis and apply it to certify infeasibility of conditional critical pairs. Combining these two results and extending the conditional confluence checker ConCon accordingly, we are able to automatically prove and certify confluence of an important class of conditional term rewrite systems

Conditional Complexity

We propose a notion of complexity for oriented conditional term rewrite systems. This notion is realistic in the sense that it measures not only successful computations but also partial computations that result in a failed rule application. A transformation to unconditional context-sensitive rewrite systems is presented which reflects this complexity notion, as well as a technique to derive runtime and derivational complexity bounds for the latter

Complexity of conditional term rewriting

We propose a notion of complexity for oriented conditional term rewrite systems satisfying certain restrictions. This notion is realistic in the sense that it measures not only successful computations, but also partial computations that result in a failed rule application. A transformation to unconditional context-sensitive rewrite systems is presented which reflects this complexity notion, as well as a technique to derive runtime and derivational complexity bounds for the result of this transformation.Comment: This is an extended and improved version of "Conditional Complexity" as published in the proceedings of RTA 2015. It has been submitted for journal publication in LMC

Dynamic human and avatar facial expressions elicit differential brain responses

Computer-generated characters, so-called avatars, are widely used in advertising, entertainment, human-computer interaction or as research tools to investigate human emotion perception. However, brain responses to avatar and human faces have scarcely been studied to date. As such, it remains unclear whether dynamic facial expressions of avatars evoke different brain responses than dynamic facial expressions of humans. In this study, we designed anthropomorphic avatars animated with motion tracking and tested whether the human brain processes fearful and neutral expressions in human and avatar faces differently. Our fMRI results showed that fearful human expressions evoked stronger responses than fearful avatar expressions in the ventral anterior and posterior cingulate gyrus, the anterior insula, the anterior and posterior superior temporal sulcus, and the inferior frontal gyrus. Fearful expressions in human and avatar faces evoked similar responses in the amygdala. We did not find different responses to neutral human and avatar expressions. Our results highlight differences, but also similarities in the processing of fearful human expressions and fearful avatar expressions even if they are designed to be highly anthropomorphic and animated with motion tracking. This has important consequences for research using dynamic avatars, especially when processes are investigated that involve cortical and subcortical regions