Related papers: A Verified Efficient Implementation of the Weighte…

We introduce a reduction order called the weighted path order (WPO) that subsumes many existing reduction orders. WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by a wide class of…

Monotonic semantic path orders and weighted path orders are powerful reduction orders for proving termination of term rewrite systems. In this paper we present their simple unification as reduction orders and reduction pairs. We also…

This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…

We show how polynomial path orders can be employed efficiently in conjunction with weak innermost dependency pairs to automatically certify polynomial runtime complexity of term rewrite systems and the polytime computability of the…

Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an…

The weighted OWA (WOWA) is a function that aggregates a set of values with weights assigned based on the rank and relative importance of each value. The weighted OWA of uncertain objective functions can generalize many of the criteria that…

This paper describes the implementation and techniques of the Nagoya Termination Tool, a termination prover for term rewrite systems. The main features of the tool are: the first implementation of the weighted path order which subsumes most…

We lift the computability path order and its extensions from plain higher-order rewriting to higher-order rewriting on beta-eta-normal forms where matching modulo beta-eta is employed. The resulting order NCPO is shown to be useful on…

Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we…

The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While…

We propose a sound and complete proof rule ProbTA for quantitative analysis of violation probability of probabilistic programs. Our approach extends the technique of trace abstraction with probability in the control-flow randomness style,…

Probabilistic pushdown automata (pPDA) are a natural operational model for a variety of recursive discrete stochastic processes. In this paper, we study certificates - succinct and easily verifiable proofs - for upper and lower bounds on…

In many statistical applications, particularly in clinical studies, hypotheses may carry different levels of importance, motivating the use of weighted multiple testing procedures (wMTPs) to control the familywise error rate (FWER). Among…

Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…

We introduce efficient algorithms for finding the $k$ shortest paths of a weighted pushdown automaton (WPDA), a compact representation of a weighted set of strings with potential applications in parsing and machine translation. Both of our…

We present a construction of a certain infinite complete partial order (CPO) that differs from the standard construction used in Scott's denotational semantics. In addition, we construct several other infinite CPO's. For some of those, we…

We address the problem of verifying safety properties of concurrent programs running over the Total Store Order (TSO) memory model. Known decision procedures for this model are based on complex encodings of store buffers as lossy channels.…

Weighted timed automata (WTA) model quantitative aspects of real-time systems like continuous consumption of memory, power or financial resources. They accept quantitative timed languages where every timed word is mapped to a value, e.g., a…

Probabilistic pushdown automata (pPDA) are a standard model for discrete probabilistic programs with procedures and recursion. In pPDA, many quantitative properties are characterized as least fixpoints of polynomial equation systems. In…

We consider a certifiable object pose estimation problem, where -- given a partial point cloud of an object -- the goal is to not only estimate the object pose, but also to provide a certificate of correctness for the resulting estimate.…