Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs

In this paper, we present a general methodology to solve a wide variety of classical lattice path counting problems in a uniform way. These counting problems are related to Dyck paths, Motzkin paths and some generalizations. The methodology uses weighted automata, equations of ordinary generating functions and continued fractions. This new methodology is called Counting Automata Methodology. It is a variation of the technique proposed by Rutten, which is called Coinductive Counting

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

Composable Probabilistic Inference with Blaise

Probabilistic inference provides a unified, systematic framework for specifying and solving these problems. Recent work has demonstrated the great value of probabilistic models defined over complex, structured domains. However, our ability to imagine probabilistic models has far outstripped our ability to programmatically manipulate them and to effectively implement inference, limiting the complexity of the problems that we can solve in practice.This thesis presents Blaise, a novel framework for composable probabilistic modeling and inference, designed to address these limitations. Blaise has three components: * The Blaise State-Density-Kernel (SDK) graphical modeling language that generalizes factor graphs by: (1) explicitly representing inference algorithms (and their locality) using a new type of graph node, (2) representing hierarchical composition and repeated substructures in the state space, the interest distribution, and the inference procedure, and (3) permitting the structure of the model to change during algorithm execution. * A suite of SDK graph transformations that may be used to extend a model (e.g. to construct a mixture model from a model of a mixture component), or to make inference more effective (e.g. by automatically constructing a parallel tempered version of an algorithm or by exploiting conjugacy in a model). * The Blaise Virtual Machine, a runtime environment that can efficiently execute the stochastic automata represented by Blaise SDK graphs. Blaise encourages the construction of sophisticated models by composing simpler models, allowing the designer to implement and verify small portions of the model and inference method, and to reuse model components from one task to another. Blaise decouples the implementation of the inference algorithm from the specification of the interest distribution, even in cases (such as Gibbs sampling) where the shape of the interest distribution guides the inference. This gives modelers the freedom to explore alternate models without slow, error-prone reimplementation. The compositional nature of Blaise enables novel reinterpretations of advanced Monte Carlo inference techniques (such as parallel tempering) as simple transformations of Blaise SDK graphs.In this thesis, I describe each of the components of the Blaise modeling framework, as well as validating the Blaise framework by highlighting a variety of contemporary sophisticated models that have been developed by the Blaise user community. I also present several surprising findings stemming from the Blaise modeling framework, including that an Infinite Relational Model can be built using exactly the same inference methods as a simple mixture model, that constructing a parallel tempered inference algorithm should be a point-and-click/one-line-of-code operation, and that Markov chain Monte Carlo for probabilistic models with complicated long-distance dependencies, such as a stochastic version of Scheme, can be managed using standard Blaise mechanisms

Composable probabilistic inference with BLAISE

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 185-190).If we are to understand human-level cognition, we must understand how the mind finds the patterns that underlie the incomplete, noisy, and ambiguous data from our senses and that allow us to generalize our experiences to new situations. A wide variety of commercial applications face similar issues: industries from health services to business intelligence to oil field exploration critically depend on their ability to find patterns in vast amounts of data and use those patterns to make accurate predictions. Probabilistic inference provides a unified, systematic framework for specifying and solving these problems. Recent work has demonstrated the great value of probabilistic models defined over complex, structured domains. However, our ability to imagine probabilistic models has far outstripped our ability to programmatically manipulate them and to effectively implement inference, limiting the complexity of the problems that we can solve in practice. This thesis presents BLAISE, a novel framework for composable probabilistic modeling and inference, designed to address these limitations. BLAISE has three components: * The BLAISE State-Density-Kernel (SDK) graphical modeling language that generalizes factor graphs by: (1) explicitly representing inference algorithms (and their locality) using a new type of graph node, (2) representing hierarchical composition and repeated substructures in the state space, the interest distribution, and the inference procedure, and (3) permitting the structure of the model to change during algorithm execution. * A suite of SDK graph transformations that may be used to extend a model (e.g. to construct a mixture model from a model of a mixture component), or to make inference more effective (e.g. by automatically constructing a parallel tempered version of an algorithm or by exploiting conjugacy in a model).(cont.) * The BLAISE Virtual Machine, a runtime environment that can efficiently execute the stochastic automata represented by BLAISE SDK graphs. BLAISE encourages the construction of sophisticated models by composing simpler models, allowing the designer to implement and verify small portions of the model and inference method, and to reuse mode components from one task to another. BLAISE decouples the implementation of the inference algorithm from the specification of the interest distribution, even in cases (such as Gibbs sampling) where the shape of the interest distribution guides the inference. This gives modelers the freedom to explore alternate models without slow, error-prone reimplementation. The compositional nature of BLAISE enables novel reinterpretations of advanced Monte Carlo inference techniques (such as parallel tempering) as simple transformations of BLAISE SDK graphs. In this thesis, I describe each of the components of the BLAISE modeling framework, as well as validating the BLAISE framework by highlighting a variety of contemporary sophisticated models that have been developed by the BLAISE user community. I also present several surprising findings stemming from the BLAISE modeling framework, including that an Infinite Relational Model can be built using exactly the same inference methods as a simple mixture model, that constructing a parallel tempered inference algorithm should be a point-and-click/one-line-of-code operation, and that Markov chain Monte Carlo for probabilistic models with complicated long-distance dependencies, such as a stochastic version of Scheme, can be managed using standard BLAISE mechanisms.by Keith Allen Bonawitz.Ph.D

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Image Evolution Using 2D Power Spectra

Procedurally generated textures have seen use in many applications, are a high-interest topic when exploring evolutionary algorithms, and hold a central interest for digital art. However, there is an existing difficulty in finding suitable heuristics for measuring perceived qualities of an image. Particular difficulty remains for quantifying aspects of style and shape. In an attempt to bridge the divide between computer vision and cognitive perception, one set of proposed measures from previous studies relate to image spatial frequencies. Based on existing research which uses power spectral density of spatial frequencies as an effective metric for image classification and retrieval, we believe this measure and others based on Fourier decomposition may be effective for guiding evolutionary texture synthesis. We briefly compare some alternative means of using frequency analysis to guide evolution of shape and composition, and refine fitness measures based on Fourier analysis and spatial frequency. Our exploration has been conducted with the goals of improving intuition of these measures, evaluating the utility of these measures for image composition, and observing possible adaptations of their use in digital evolutionary art. Multiple evolutionary guidance schemes with consideration of the spatial frequencies' power spectra and phase have been evaluated across numerous targets with mixed results. We will display our exploration of power spectral density measures and their effectiveness as used for evolutionary algorithm fitness targets, particularly for basic compositional guidance in evolutionary art. We also observe and analyze a previously identified phenomenon of spatial properties which could lead to further consideration of visual comfort and aesthetics