Related papers: Loops under Strategies ... Continued
In this paper we use the decreasing diagrams technique to show that a left-linear term rewrite system R is confluent if all its critical pairs are joinable and the critical pair steps are relatively terminating with respect to R. We further…
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
When a system sends messages through a lossy channel, then the language encoding all sequences of messages can be abstracted by its downward closure, i.e. the set of all (not necessarily contiguous) subwords. This is useful because even if…
Rewriting logic and its implementation Maude are an expressive framework for the formal specification and verification of software and other kinds of systems. Concurrency is naturally represented by nondeterministic local transformations…
In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…
Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher order…
Hierarchical decomposition of control is unavoidable in large dynamical systems. In reinforcement learning (RL), it is usually solved with subgoals defined at higher policy levels and achieved at lower policy levels. Reaching these goals…
The safety of our day-to-day life depends crucially on the correct functioning of embedded software systems which control the functioning of more and more technical devices. Many of these software systems are time-critical. Hence,…
We establish that all strategy-proof social choice rules in strict preference domains follow necessarily a two-step procedure. In the first step, agents are asked to reveal some specific information about their preferences. Afterwards, a…
We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to…
Large Reasoning Models (LRMs) achieve strong performance on mathematical reasoning tasks but remain unreliable on challenging instances. Existing test-time scaling methods, such as repeated sampling, self-correction, and tree search,…
Lengthy evaluation times are common in many optimization problems such as direct policy search tasks, especially when they involve conducting evaluations in the physical world, e.g. in robotics applications. Often when evaluating solution…
Dependency pairs are one of the most powerful techniques to analyze termination of term rewrite systems (TRSs) automatically. We adapt the dependency pair framework to the probabilistic setting in order to prove almost-sure innermost…
We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover,…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
We introduce a method of verifying termination of logic programs with respect to concrete queries (instead of abstract query patterns). A necessary and sufficient condition is established and an algorithm for automatic verification is…
Large Reasoning Models (LRMs) achieve strong performance by generating long reasoning traces with reflection. Through a large-scale empirical analysis, we find that a substantial fraction of reflective steps consist of self-verification…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
The objective of this paper is to present general, mechanically verified, refinement rules for reasoning about recursive programs and while loops in the context of concurrency. Unlike many approaches to concurrency, we do not assume that…