Related papers: On the Termination Problem for Probabilistic Highe…
Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system $R$,…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
This paper presents a wp-style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sided bounds for such expectations, and show the…
We address the problem of statically checking safety properties (such as assertions or deadlocks) for parameterized phaser programs. Phasers embody a non-trivial and modern synchronization construct used to orchestrate executions of…
We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a…
We study an extension of the Arrival problem, called Recursive Arrival, inspired by Recursive State Machines, which allows for a family of switching graphs that can call each other in a recursive way. We study the computational complexity…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They are the simplest common model of concurrent programs that allows unbounded spawning of processes. In the probabilistic version of BPPs, every process generates…
This article presents the complexity of reachability decision problems for parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a…
Probabilistic model checking computes probabilities and expected values related to designated behaviours of interest in Markov models. As a formal verification approach, it is applied to critical systems; thus we trust that probabilistic…
We examine a constrained Markov decision process under uncertain transition probabilities, with the uncertainty modeled as deviations from observed transition probabilities. We construct the uncertainty set associated with the deviations…
Higher-order modal fixpoint logic (HFL) is a higher-order extension of the modal mu-calculus, and strictly more expressive than the modal mu-calculus. It has recently been shown that various program verification problems can naturally be…
This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…
We study linear time model checking of collapsible higher-order pushdown systems (CPDS) of order 2 (manipulating stack of stacks) against MSO and PDL (propositional dynamic logic with converse and loop) enhanced with push/pop matching…
We present Coneris, the first higher-order concurrent separation logic for reasoning about error probability bounds of higher-order concurrent probabilistic programs with higher-order state. To support modular reasoning about concurrent…
Universal probabilistic programming languages (PPLs) make it relatively easy to encode and automatically solve statistical inference problems. To solve inference problems, PPL implementations often apply Monte Carlo inference algorithms…
Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of…
The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…
In this work we prove decidability of the model-checking problem for safe recursion schemes against properties defined by alternating B-automata. We then exploit this result to show how to compute downward closures of languages of finite…
Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…