Abstract. We introduce ICE, a robust learning paradigm for synthesizing invariants, that learns using examples, counter-examples, and implications, and show that it admits honest teachers and strongly convergent mechanisms for invariant synthesis. We observe that existing algorithms for black-box abstract interpretation can be interpreted as ICE-learning algorithms. We develop new strongly convergent ICE-learning algorithms for two domains, one for learning Boolean combinations of numerical invariants for scalar variables and one for quantified invariants for arrays and dynamic lists. We implement these ICE-learning algorithms in a verification tool and show they are robust, practical, and efficient.
Inductive invariants can be robustly synthesized using a learning model where the teacher is a program verifier who instructs the learner through concrete program configurations, classified as positive, negative, and implications. We propose the first learning algorithms in this model with implication counterexamples that are based on machine learning techniques. In particular, we extend classical decision-tree learning algorithms in machine learning to handle implication samples, building new scalable ways to construct small decision trees using statistical measures. We also develop a decision-tree learning algorithm in this model that is guaranteed to converge to the right concept (invariant) if one exists. We implement the learners and an appropriate teacher, and show that the resulting invariant synthesis is efficient and convergent for a large suite of programs.
Research Summary: While research has focused primarily on stars as individual contributors, we examine organizational situations where stars must work closely with non‐stars. We argue that, in such situations, building teamwork around a star is an exercise in learning under complexity. In response, organizations prioritize interactions involving the star to simplify learning. This simplification, however, creates organizational myopia. We claim that a star’s temporary absence helps the organization overcome myopia by triggering a search for new routines. When he returns, the organization may combine these new routines with pre‐absence routines to improve teamwork and performance. We exploit injuries to star players in the National Basketball Association as an exogenous shock and find that on average, teams perform better after a star’s return than before his absence. Managerial Summary: This study examines the effect of the temporary absence of a star employee on organizational performance. We find evidence that a star employee’s temporary absence helps the organization overcome an over‐reliance on the star and improve teamwork. Improved teamwork, in turn, enables the organization to perform better upon the star’s return than it did prior to his absence. This result suggests that organizations might want to revisit the tendency to view stars as too valuable to lose, even for a short time. In particular, organizations may want to pull stars from ongoing projects and encourage them to attend professional development programs. A star’s temporary absence and return from such a program improves not only the star’s skills but also the organization’s teamwork.
This study uses data from the National Basketball Association to explore organizational mechanisms that affect the division of firm surplus in human-capital-intensive activity. It builds on the idea that reciprocal interdependence among team members creates the potential for complementarity. Complementarity, in turn, translates into higher firm surplus. The division of this surplus is subject to bargaining between the firm owner and labor. We argue that when complementarity increases, the firm owner's share of surplus will grow if interdependence among team members is symmetric. Furthermore, we identify three levers that make complementarity amenable to managerial design: the nature of interaction among team members, the relative dominance of team members, and the composition of a team. We find that greater interaction among team members and higher recruitment of team-oriented individuals are associated with increased complementarity, whereas dominant team members are associated with reduced complementarity. The study contributes to the literature on organization design by extending its implications to the division of surplus in human-capital-intensive activity.
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