Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

Benchmarks for Parity Games (extended version)

We propose a benchmark suite for parity games that includes all benchmarks that have been used in the literature, and make it available online. We give an overview of the parity games, including a description of how they have been generated. We also describe structural properties of parity games, and using these properties we show that our benchmarks are representative. With this work we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from https://github.com/jkeiren/paritygame-generator. This is an extended version of the paper that has been accepted for FSEN 201

On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms

Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices. Likewise, uniquely typable skeletons of closed lambda terms predetermine the unique simply-typed lambda term that can be obtained by labeling their leaves with de Bruijn indices. We derive, through a sequence of logic program transformations, efficient code for their combinatorial generation and study their statistical properties. As a result, we obtain context-free grammars describing closable and uniquely closable skeletons of lambda terms, opening the door for their in-depth study with tools from analytic combinatorics. Our empirical study of the more difficult case of (uniquely) typable terms reveals some interesting open problems about their density and asymptotic behavior. As a connection between the two classes of terms, we also show that uniquely typable closed lambda term skeletons of size $3n+1$ are in a bijection with binary trees of size $n$.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Probabilistic Logic Programming with Beta-Distributed Random Variables

We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly specified and engineered domains, while simultaneously we maintain the flexibility offered by aProbLog in handling complex relational domains. Our motivation is that faithfully capturing the distribution of probabilities is necessary to compute an expected utility for effective decision making under uncertainty: unfortunately, these probability distributions can be highly uncertain due to sparse data. To understand and accurately manipulate such probability distributions we need a well-defined theoretical framework that is provided by the Beta distribution, which specifies a distribution of probabilities representing all the possible values of a probability when the exact value is unknown.Comment: Accepted for presentation at AAAI 201

Condition/Decision Duality and the Internal Logic of Extensive Restriction Categories

In flowchart languages, predicates play an interesting double role. In the textual representation, they are often presented as conditions, i.e., expressions which are easily combined with other conditions (often via Boolean combinators) to form new conditions, though they only play a supporting role in aiding branching statements choose a branch to follow. On the other hand, in the graphical representation they are typically presented as decisions, intrinsically capable of directing control flow yet mostly oblivious to Boolean combination. While categorical treatments of flowchart languages are abundant, none of them provide a treatment of this dual nature of predicates. In the present paper, we argue that extensive restriction categories are precisely categories that capture such a condition/decision duality, by means of morphisms which, coincidentally, are also called decisions. Further, we show that having these categorical decisions amounts to having an internal logic: Analogous to how subobjects of an object in a topos form a Heyting algebra, we show that decisions on an object in an extensive restriction category form a De Morgan quasilattice, the algebraic structure associated with the (three-valued) weak Kleene logic $\mathbf{K}^w_3$. Full classical propositional logic can be recovered by restricting to total decisions, yielding extensive categories in the usual sense, and confirming (from a different direction) a result from effectus theory that predicates on objects in extensive categories form Boolean algebras. As an application, since (categorical) decisions are partial isomorphisms, this approach provides naturally reversible models of classical propositional logic and weak Kleene logic.Comment: 19 pages, including 6 page appendix of proofs. Accepted for MFPS XXX

Formalized proof, computation, and the construction problem in algebraic geometry

An informal discussion of how the construction problem in algebraic geometry motivates the search for formal proof methods. Also includes a brief discussion of my own progress up to now, which concerns the formalization of category theory within a ZFC-like environment

On the enumeration of closures and environments with an application to random generation

Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environments and closures, namely the so-called plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size $n$. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environemnts and closures