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Control Barrier Functions (CBFs) allow for efficient synthesis of controllers to maintain desired invariant properties of safety-critical systems. However, the problem of identifying a CBF remains an open question. As such, this paper…
This work introduces (1) a technique that allows large language models (LLMs) to leverage user-provided code when solving programming tasks and (2) a method to iteratively generate modular sub-functions that can aid future code generation…
We aim at investigating the solvability/insolvability of nondeterministic logarithmic-space (NL) decision, search, and optimization problems parameterized by natural size parameters using simultaneously polynomial time and sub-linear space.…
Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning…
This letter proposes a learning-based bounded synthesis for a semi-Markov decision process (SMDP) with a linear temporal logic (LTL) specification. In the product of the SMDP and the deterministic $K$-co-B\"uchi automaton (d$K$cBA)…
Large language models (LLMs) have enabled a range of applications in zero-shot and few-shot learning settings, including the generation of synthetic datasets for training and testing. However, to reliably use these synthetic datasets, it is…
Symmetries are intrinsic to many combinatorial problems including Boolean Satisfiability (SAT) and Constraint Programming (CP). In SAT, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique…
Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their…
Iterative first-order methods such as gradient descent and its variants are widely used for solving optimization and machine learning problems. There has been recent interest in analytic or numerically efficient methods for computing…
Reactive synthesis is a technology for the automatic construction of reactive systems from logical specifications. In these lecture notes, we study different algorithms for the reactive synthesis problem of linear-time temporal logic (LTL).…
Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations…
System Level Synthesis (SLS) parametrization facilitates controller synthesis for large, complex, and distributed systems by incorporating system level constraints (SLCs) into a convex SLS problem and mapping its solution to stable…
This paper presents a systematic method for synthesizing a Control Barrier Function (CBF) that encodes predictive information into a CBF. Unlike other methods, the synthesized CBF can account for changes and time-variations in the…
Let $\mathsf{TH}_k$ denote the $k$-out-of-$n$ threshold function: given $n$ input Boolean variables, the output is $1$ if and only if at least $k$ of the inputs are $1$. We consider the problem of computing the $\mathsf{TH}_k$ function…
Numerous math benchmarks exist to evaluate LLMs' mathematical capabilities. However, most involve extensive manual effort and are difficult to scale. Consequently, they cannot keep pace with LLM development or easily provide new instances…
It is often difficult to correctly implement a Boolean controller for a complex system, especially when concurrency is involved. Yet, it may be easy to formally specify a controller. For instance, for a pipelined processor it suffices to…
We address the problem of latent truth discovery, LTD for short, where the goal is to discover the underlying true values of entity attributes in the presence of noisy, conflicting or incomplete information. Despite a multitude of…
Boolean Satisfiability (SAT) is arguably the archetypical NP-complete decision problem. Progress in SAT solving algorithms has motivated an ever increasing number of practical applications in recent years. However, many practical uses of…
We propose an approach to synthesize linear feedback controllers for linear systems in polygonal environments. Our method focuses on designing a robust controller that can account for uncertainty in measurements. Its inputs are provided by…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…