Related papers: Forward analysis for WSTS, Part I: Completions
We present highly optimized data structures for the dynamic predecessor problem, where the task is to maintain a set $S$ of $w$-bit numbers under insertions, deletions, and predecessor queries (return the largest element in $S$ no larger…
The set of two-body reduced states of translation invariant, infinite quantum spin chains can be approximated from inside and outside using matrix product states and marginals of finite systems, respectively. These lead to hierarchies of…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…
We show that completeness at higher levels of the theory of the reals is a robust notion (under changing the signature and bounding the domain of the quantifiers). This mends recognized gaps in the hierarchy, and leads to stronger…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
Transition systems (TS) and Petri nets (PN) are important models of computation ubiquitous in formal methods for modeling systems. An important problem is how to extract from a given TS a PN whose reachability graph is equivalent (with a…
To analyze high-dimensional systems, many fields in science and engineering rely on high-level descriptions, sometimes called "macrostates," "coarse-grainings," or "effective theories". Examples of such descriptions include the…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
Moment systems arise in a wide range of contexts and applications, e.g. in network modeling of complex systems. Since moment systems consist of a high or even infinite number of coupled equations, an indispensable step in obtaining a…
State space is widely used for modeling power systems and analyzing their dynamics but it is limited to representing causal and proper systems in which the number of zeros does not exceed the number of poles. In other words, the system…
Labelled Transition Systems (LTSs) are a fundamental semantic model in many areas of informatics, especially concurrency theory. Yet, reasoning on LTSs and relations between their states can be difficult and elusive: very simple process…
This paper presents identities for calculating over-approximated successor sets of discrete-time nonlinear systems using hybrid zonotopes. The proposed technique extends the state-update set construct, previously developed for linear hybrid…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
Not all contracts are good, but all good contracts can be expressed as a finite-state transition system ("State-Transition Contracts"). Contracts that can be represented as State-Transition Contracts discretize fat-tailed risk to…
Uncertain information is commonplace in real-world data management scenarios. The ability to represent large sets of possible instances (worlds) while supporting efficient storage and processing is an important challenge in this context.…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
We develop domain theory in constructive univalent foundations without Voevodsky's resizing axioms. In previous work in this direction, we constructed the Scott model of PCF and proved its computational adequacy, based on directed complete…