Related papers: Axiomatizing Hybrid XPath with Data
We use the theory of algebraic effects to give a complete equational axiomatization for dynamic threads. Our method is based on parameterized algebraic theories, which give a concrete syntax for strong monads on functor categories, and are…
A symmetry of a dynamical system is a map that transforms one trajectory to another trajectory. We introduce a new type of abstraction for hybrid automata based on symmetries. The abstraction combines different modes in a concrete automaton…
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…
Probabilistic behavior is omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of various reasons, like uncertain environments, or fundamental properties of nature. In this paper, we…
We show NP-completeness for various problems about the existence of arithmetic expression trees. When given a set of operations, inputs, and a target value does there exist an expression tree with those inputs and operations that evaluates…
This paper proposes a notion of branching bisimilarity for non-deterministic probabilistic processes. In order to characterize the corresponding notion of rooted branching probabilistic bisimilarity, an equational theory is proposed for a…
Reachability analysis for hybrid systems is an active area of development and has resulted in many promising prototype tools. Most of these tools allow users to express hybrid system as automata with a set of ordinary differential equations…
A subclass of nondeterministic Finite Automata generated by means of regular Grammars (GFAs, for short) is introduced. A process algebra is proposed, whose semantics maps a term to a GFA. We prove a representability theorem: for each GFA…
Verification of programs operating on heap-allocated data structures, for instance lists or trees, poses significant challenges due to the potentially unbounded size of such data structures. We present time-indexed heap invariants, a novel…
Complex network data is prevalent in various real-world domains, including physical, technological, and biological systems. Despite this prevalence, predicting trends and understanding behavioral patterns in complex systems remain…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…
This article proves the completeness of an axiomatization for initial value problems (IVPs) with compact initial conditions and compact time horizons for bounded open safety, open liveness and existence properties. Completeness…
XPath is a simple language for navigating an XML-tree and returning a set of answer nodes. The focus in this paper is on the complexity of the containment problem for various fragments of XPath. We restrict attention to the most common…
Designing programming languages that enable intuitive and safe manipulation of data structures is a critical research challenge. Conventional destructive memory operations using pointers are complex and prone to errors. Existing type…
The need to model and analyse dynamic systems operating over complex data is ubiquitous in AI and neighboring areas, in particular business process management. Analysing such data-aware systems is a notoriously difficult problem, as they…
This paper proves that the equational theory of the class $RA_{\alpha}^{csp}$ of representable polyadic algebras is finitely axiomatizable over its substitution-free reduct $RA_{\alpha}^{cp}$, for finite $\alpha$. That is, substitutions of…
A combination of hierarchical tree-like data structures and data access patterns from fast multipole methods and hierarchical low-rank approximation of linear operators from H-matrix methods appears to form an algorithmic path forward for…
Data automata on data words is a decidable model proposed by Boja\'nczyk et al. in 2006. Class automata, introduced recently by Boja\'nczyk and Lasota, is an extension of data automata which unifies different automata models on data words.…
In earlier work, the Abstract State Machine Thesis -- that arbitrary algorithms are behaviorally equivalent to abstract state machines -- was established for several classes of algorithms, including ordinary, interactive, small-step…