High-throughput genomic data reveal thousands of gene variants per patient, and it is often difficult to determine which of these variants underlies disease in a given individual. However, at the population level, there may be some degree of phenotypic homogeneity, with alterations of specific physiological pathways underlying the pathogenesis of a particular disease. We describe here the human gene connectome (HGC) as a unique approach for human Mendelian genetic research, facilitating the interpretation of abundant genetic data from patients with the same disease, and guiding subsequent experimental investigations. We first defined the set of the shortest plausible biological distances, routes, and degrees of separation between all pairs of human genes by applying a shortest distance algorithm to the full human gene network. We then designed a hypothesis-driven application of the HGC, in which we generated a Toll-like receptor 3-specific connectome useful for the genetic dissection of inborn errors of Toll-like receptor 3 immunity. In addition, we developed a functional genomic alignment approach from the HGC. In functional genomic alignment, the genes are clustered according to biological distance (rather than the traditional molecular evolutionary genetic distance), as estimated from the HGC. Finally, we compared the HGC with three state-of-the-art methods: String, FunCoup, and HumanNet. We demonstrated that the existing methods are more suitable for polygenic studies, whereas HGC approaches are more suitable for monogenic studies. The HGC and functional genomic alignment data and computer programs are freely available to noncommercial users from http://lab.rockefeller.edu/casanova/HGC and should facilitate the genome-wide selection of disease-causing candidate alleles for experimental validation.

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This work introduces a motion-planning framework for a hybrid system with general continuous dynamics to satisfy a temporal logic specification consisting of co-safety and safety components in a partially unknown environment. The framework employs a multi-layered synergistic planner to generate trajectories that satisfy the specification and adopts an iterative replanning strategy to deal with unknown obstacles. When the discovery of an obstacle renders the specification unsatisfiable, a division between the constraints in the specification is considered. The co-safety component of the specification is treated as a soft constraint, whose partial satisfaction is allowed, while the safety component is viewed as a hard constraint, whose violation is forbidden. To partially satisfy the co-safety component, inspirations

Boolean functional synthesis is the process of constructing a Boolean function from a Boolean specification that relates input and output variables. Despite significant recent developments in synthesis algorithms, Boolean functional synthesis remains a challenging problem even when state-of-the-art methods are used for decomposing the specification. In this work we bring a fresh decomposition approach, orthogonal to existing methods, that explores the decomposition of the specification into separate input and output components. We make use of an input-output decomposition of a given specification described as a CNF formula, by alternatingly analyzing the separate input and output components. We exploit well-defined properties of these components to ultimately synthesize a solution for the entire specification. We first provide a theoretical result that, for input components with specific structures, synthesis for CNF formulas via this framework can be performed more efficiently than in the general case. We then show by experimental evaluations that our algorithm performs well also in practice on instances which are challenging for existing state-of-the-art tools, serving as a good complement to modern synthesis techniques.

The specification of complex motion goals through temporal logics is increasingly favored in robotics to narrow the gap between task and motion planning. A major limiting factor of such logics, however, is their Boolean satisfaction condition. To relax this limitation, we introduce a method for quantifying the satisfaction of co-safe linear temporal logic specifications, and propose a planner that uses this method to synthesize robot trajectories with the optimal satisfaction value. The method assigns costs to violations of specifications from user-defined proposition costs. These violation costs define a distance to satisfaction and can be computed algorithmically using a weighted automaton. The planner utilizes this automaton and an abstraction of the robotic system to construct a product graph that captures all possible robot trajectories and their distances to satisfaction. Then, a plan with the minimum distance to satisfaction is generated by employing this graph as the high-level planner in a synergistic planning framework. The efficacy of the method is illustrated on a robot with unsatisfiable specifications in an office environment.

The Canadian traveler problem (CTP) is the problem of traversing a given graph, where some of the edges may be blocked -a state which is revealed only upon reaching an incident vertex. Originally stated by Papadimitriou and Yannakakis (1991), the adversarial version of CTP was shown to be PSPACE-complete, with the stochastic version shown to be #P-hard.We show that stochastic CTP is also PSPACE-complete: initially proving PSPACE-hardness for the dependent version of stochastic CTP, and proceeding with gadgets that allow us to extend the proof to the independent case.Since for disjoint-path graphs, CTP can be solved in polynomial time, we examine the complexity of the more general remote-sensing CTP, and show that it is NP-hard even for disjoint-path graphs.probability p(e). The actual state of each edge e ∈ E becomes known only upon reaching a vertex incident on e. Traversing an unblocked edge e incurs a non-negative cost equal to the weight of e. The problem is to find a policy π that minimizes the expected traversal cost C(π) from s to t.CTP formalizes a basic question of navigating in a partially known environment, which is a fundamental task for transportation, autonomous robotic systems, computer games, and more. Other variants of CTP have been introduced and analyzed in the research literature [2,3,4]. There has been a strong recent resurgence of interest in CTP, both theoretical [5,6] and empirical [7,8,9]. A preliminary alternative proof of Theorem 2 appears in an unpublished work by one of the authors [10].When originally introduced in [1], two variants were examined: the adversarial variant and the stochastic variant. The adversarial variant was shown to be PSPACE-complete by reduction from QSAT. For the stochastic version, membership in PSPACE was shown, however only #P-hardness was established by reduction from the st-reliability problem, leaving the question of PSPACE-hardness open. Apparently proving the stronger result requires some form of dependency between the edges, achieved "through the back door" in the adversarial variant. This paper settles the question, showing that CTP is indeed PSPACE-complete.Since the size of an optimal policy is potentially exponential in the size of the problem description, we in fact show that it is PSPACE-hard to find even the optimal first action at s.We begin with a variant of CTP with dependent directed edges, CTP-Dep, which allows for a simple proof of PSPACE-hardness by reduction from QSAT, before proceeding with the proof for the "standard" stochastic CTP. Although the latter result subsumes the former, proving the dependent CTP result first greatly simplifies the intuition behind the proof of the standard case.Another variant we explore is remote-sensing CTP, henceforth called Sensing-CTP, in which additional actions called remote-sensing actions are allowed. Each such action reveals, for a certain cost, the status of a nonincident edge. Recently it was shown [9] that stochastic CTP can be solved in low-order polynomial time on disjoint-path graphs. It was b...

The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple and natural formalization of sequential decomposition, in which a task is decomposed into two sequential sub-tasks, with the first sub-task to be executed before the second sub-task is executed. These tasks are specified by means of input/output relations. We define and study decomposition problems, which is to decide whether a given specification can be sequentially decomposed. Our main result is that decomposition itself is a difficult computational problem. More specifically, we study decomposition problems in three settings: where the input task is specified explicitly, by means of Boolean circuits, and by means of automatic relations. We show that in the first setting decomposition is NP-complete, in the second setting it is NEXPTIME-complete, and in the third setting there is evidence to suggest that it is undecidable. Our results indicate that the intuitive idea of decomposition as a system-design approach requires further investigation. In particular, we show that adding a human to the loop by asking for a decomposition hint lowers the complexity of decomposition problems considerably.

In the Adapter Design Pattern, a programmer implements a Target interface by constructing an Adapter that accesses an existing Adaptee code. In this work, we present a reactive synthesis interpretation to the adapter design pattern, wherein an algorithm takes an Adaptee and a Target transducers, and the aim is to synthesize an Adapter transducer that, when composed with the Adaptee, generates a behavior that is equivalent to the behavior of the Target. One use of such an algorithm is to synthesize controllers that achieve similar goals on different hardware platforms. While this problem can be solved with existing synthesis algorithms, current state-of-the-art tools fail to scale. To cope with the computational complexity of the problem, we introduce a special form of specification format, called Separated GR(k), which can be solved with a scalable synthesis algorithm but still allows for a large set of realistic specifications. We solve the realizability and the synthesis problems for Separated GR(k), and show how to exploit the separated nature of our specification to construct better algorithms, in terms of time complexity, than known algorithms for GR(k) synthesis. We then describe a tool, called SGR(k), that we have implemented based on the above approach and show, by experimental evaluation, how our tool outperforms current state-of-the-art tools on various benchmarks and test-cases.