Resolution cannot polynomially simulate compressed-BFS

Many algorithms for Boolean satisfiability (SAT) work within the framework of resolution as a proof system, and thus on unsatisfiable instances they can be viewed as attempting to find proofs by resolution. However it has been known since the 1980s that every resolution proof of the pigeonhole principle (PHP n m ), suitably encoded as a CNF instance, includes exponentially many steps [18]. Therefore SAT solvers based upon the DLL procedure [12] or the DP procedure [13] must take exponential time. Polynomial-sized proofs of the pigeonhole principle exist for different proof systems, but general-purpose SAT solvers often remain confined to resolution. This result is in correlation with empirical evidence. Previously, we introduced the Compressed-BFS algorithm to solve the SAT decision problem. In an earlier work [27], an implementation of a Compressed-BFS algorithm empirically solved instances in Θ( n 4 ) time. Here, we add to this claim, and show analytically that these instances are solvable in polynomial time by Compressed-BFS. Thus the class of tautologies efficiently provable by Compressed-BFS is different than that of any resolution-based procedure. We hope that the details of our complexity analysis shed some light on the proof system implied by Compressed-BFS. Our proof focuses on structural invariants within the compressed data structure that stores collections of sets of open clauses during the Compressed-BFS algorithm. We bound the size of this data structure, as well as the overall memory, by a polynomial. We then use this to show that the overall runtime is bounded by a polynomial.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41774/1/10472_2004_Article_5379427.pd

Democratizing Self-Service Data Preparation through Example Guided Program Synthesis,

The majority of real-world data we can access today have one thing in common: they are not immediately usable in their original state. Trapped in a swamp of data usability issues like non-standard data formats and heterogeneous data sources, most data analysts and machine learning practitioners have to burden themselves with "data janitor" work, writing ad-hoc Python, PERL or SQL scripts, which is tedious and inefficient. It is estimated that data scientists or analysts typically spend 80% of their time in preparing data, a significant amount of human effort that can be redirected to better goals. In this dissertation, we accomplish this task by harnessing knowledge such as examples and other useful hints from the end user. We develop program synthesis techniques guided by heuristics and machine learning, which effectively make data preparation less painful and more efficient to perform by data users, particularly those with little to no programming experience. Data transformation, also called data wrangling or data munging, is an important task in data preparation, seeking to convert data from one format to a different (often more structured) format. Our system Foofah shows that allowing end users to describe their desired transformation, through providing small input-output transformation examples, can significantly reduce the overall user effort. The underlying program synthesizer can often succeed in finding meaningful data transformation programs within a reasonably short amount of time. Our second system, CLX, demonstrates that sometimes the user does not even need to provide complete input-output examples, but only label ones that are desirable if they exist in the original dataset. The system is still capable of suggesting reasonable and explainable transformation operations to fix the non-standard data format issue in a dataset full of heterogeneous data with varied formats. PRISM, our third system, targets a data preparation task of data integration, i.e., combining multiple relations to formulate a desired schema. PRISM allows the user to describe the target schema using not only high-resolution (precise) constraints of complete example data records in the target schema, but also (imprecise) constraints of varied resolutions, such as incomplete data record examples with missing values, value ranges, or multiple possible values in each element (cell), so as to require less familiarity of the database contents from the end user.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163059/1/markjin_1.pd

Heterogeneous Self-Reconfiguring Robotics

Self-reconfiguring (SR) robots are modular systems that can autonomously change shape, or reconfigure, for increased versatility and adaptability in unknown environments. In this thesis, we investigate planning and control for systems of non-identical modules, known as heterogeneous SR robots. Although previous approaches rely on module homogeneity as a critical property, we show that the planning complexity of fundamental algorithmic problems in the heterogeneous case is equivalent to that of systems with identical modules. Primarily, we study the problem of how to plan shape changes while considering the placement of specific modules within the structure. We characterize this key challenge in terms of the amount of free space available to the robot and develop a series of decentralized reconfiguration planning algorithms that assume progressively more severe free space constraints and support reconfiguration among obstacles. In addition, we compose our basic planning techniques in different ways to address problems in the related task domains of positioning modules according to function, locomotion among obstacles, self-repair, and recognizing the achievement of distributed goal-states. We also describe the design of a novel simulation environment, implementation results using this simulator, and experimental results in hardware using a planar SR system called the Crystal Robot. These results encourage development of heterogeneous systems. Our algorithms enhance the versatility and adaptability of SR robots by enabling them to use functionally specialized components to match capability, in addition to shape, to the task at hand

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum