systems engineers

Abstract: We present the first local FPT algorithm for finding important separators: Given an undirected graph $G$ with $n$ vertices and $m$ edges, vertices $s,t$ and parameters $k$ and $ν$, we can enumerate all $s$-$t$ important separators of size at most $k$ and volume at most $ν$ in time $\tilde{O}(ν2^{O(k)})$. Known approaches spend either $Ω(m)$ time (not local) or $ν^{Ω(k)}$ time (not FPT). Using this local algorithm, we show the following applications. (1) The first is an improved construction of unbreakable decomposition, a powerful generalization of tree decompositions. For any $k$, we can compute a $(5k,k)$-unbreakable decomposition with adhesion $4k$ in $\tilde{O}(k^{O(k)}m)$ time. This strictly subsumes the result of Anand, Lee, Li, Long, and Saranurak (SODA 2025) and is faster than the recent $O(k^{O(k^2)}m)$-time algorithm by Korhonen (STOC 2025) when $k = ω\Bigl(\sqrt{\frac{\log \log n}{\log \log \log n}}\Bigr)$. Our algorithm is also simpler than that of Korhonen (STOC 2025). (2) We give a near-linear time algorithm for single-sink important separators. For any sink $t$, we can list all $v$-$t$ important separators of size at most $k$ across all $v \in V(G)$ in time $\tilde{O}(2^{O(k)}m)$. Known approaches trivially compute $v$-$t$ important separators for each $v$, taking $Ω(4^k k mn)$ time. (3) Using the above result on single-sink important separators, we speed up undirected shadow removal and give the first almost-linear time FPT algorithm for Edge Multicut.

Abstract: When any physical system executes a logically irreversible (non-injective) step of a computation, the excess heat released over the Landauer limit is an energetic cost that cannot be recovered. In modern computers this cost vastly dwarfs the Landauer cost. Modern stochastic thermodynamics refers to this cost as the ``entropy production'' and has derived fundamental lower bounds on its value. Here we introduce a thermodynamic model of circuits using heat functions and investigate its entropy production, deriving new results on the thermodynamic complexity of circuits. We first show that computing the optimal heat functions for gates in a given circuit (minimizing the entropy production) is PP-complete and multiplicative approximation of those heat functions is NP-hard, but additive approximation admits a polynomial-time randomized algorithm. We give tight bounds for entropy production for certain specific families of circuits (on uniformly distributed inputs): an $n$-ary AND tree of depth $O(\log n)$ requires $Ω(n)$ entropy production, while a serial chain achieves $O(1)$ in an idealized model, showing an energy-depth tradeoff. The Batcher odd-even mergesort network on $n$ bits has $Θ(n)$ entropy production, asymptotically less than its $Θ(n \log^2 n)$ gate count. On random permutations of distinct integers its entropy production is $Θ(n \log^2 n)$, asymptotically exceeding the Landauer cost of sorting; but preceding it with Leighton and Plaxton's almost-sorting network reduces the total heat released to $O(n \log n)$. Finally, we show how to sort $n$ values with zero circuit entropy production over any exchangeable input distribution. Our framework also yields streamlined proofs of known results in stochastic thermodynamics on mismatch cost and modularity cost.

Abstract: The central object in this work is the Boolean network, a function $f:\{0,1\}^V \to \{0,1\}^V$. Often identified with $f$ is its dynamics $D_f$, the digraph with exactly $\{x \to y : f(x)=y\}$ as its arcs. The interaction graph of $f$ is the digraph $G$ on $V$ which can be thought of as representing the dependencies of the components of $f$ on one another. On the other hand, model-checking is a major field of study in graph algorithms and complexity. We consider problems at the intersection of these paradigms: for a given property $φ$, we say that a digraph $G$ is $φ$-dynamic if $G$ is the interaction graph of some Boolean network $f$ such that $D_f \models φ$. The corresponding decision problem $φ$-DYNAMIC asks whether $G$ is $φ$-dynamic. Problems of this form are well-studied in the Boolean networks community. For example, it is a well-known result that, letting $φ$ be 'No fixed points' (i.e. $\nexists x:x\to x$), $φ$-DYNAMIC is equivalent to the structural digraph problem NON-ACYCLIC, which is solvable in linear time. We establish, for the first time, properties $φ$ for which $φ$-DYNAMIC is computationally hard. These include the 'Unique fixed point' property $\exists!x:x\to x$, and a range of properties concerning the periodic points of $f$ (i.e. vertices of $D_f$ which lie on a cycle). More widely, we exhibit an infinite family of natural properties $φ$ such that $φ$-DYNAMIC is $\mathrm{NEXPTIME}$-complete, which we call PERIOD PIECE. As a special case, these include all properties of the form 'Unique cycle of length $k$' and 'Exactly $k$ fixed points' for any $k \ge 1$. On the other hand, we show that if the input digraph has bounded in-degree, then for those same problems $φ$-DYNAMIC collapses down to $\mathrm{NP}^{\mathrm{NP}}$, the second level of the polynomial hierarchy, though it remains $\mathrm{NP}^{\mathrm{NP}}$-complete.

Abstract: Structural analysis is a core method in Petri Net (PN) research, offering a perspective complementary to state-space techniques while avoiding many of their limitations. It is well studied for classical PNs but far less for High-Level Petri Nets (HLPN). Symmetric Nets (SN), a common HLPN formalism, use compact annotations to encode behavioral symmetries, enabling the construction of a symbolic reachability graph (and a lumped Markov chain in stochastic SN) and the execution of symbolic discrete-event simulations. During the past two decades, structural techniques tailored to SN have been developed, notably supported by the SNexpression tool. This tool implements a formal calculus designed for the computation of symbolic structural relations, including, but not limited to, conflict relations and causal dependencies. Here, we focus on using this calculus to verify semi-automatically symbolic structural invariants, a task currently feasible only for certain restricted SN subclasses. We focus specifically on (semi)flows and briefly discuss an approach through which a flow generative family can be generated, at least theoretically. We further briefly outline a framework for the formal verification of a broader class of invariant properties. An extended formulation of the SN formalism is employed, which demonstrably satisfies the closure property with respect to fundamental functional operators. The core concepts are elucidated by means of representative examples throughout the exposition.

Abstract: What determines the unavoidable sample cost of learning cyclic causal structure? For cyclic linear non-Gaussian models, we study exact condensation recovery from observational data: identifying the strongly connected component (SCC) partition and all edges between components. We establish the first information-theoretic lower bounds on sample complexity for this target. For $p$ variables, maximum SCC size $s_{\max}$, and maximum external-parent count $d_B$, any estimator requires order $s_{\max}\log(ep/s_{\max})+d_B\log(ep/d_B)$ samples in the worst case over a regular model class. These bounds distinguish the costs of SCC membership and external-parent selection. Under principal invertibility and without correlation faithfulness, we establish a population block-exogeneity principle that identifies unknown root SCCs through residual independence and inclusion minimality. A sparse-adjustment characterization shows that small adjustment sets suffice to identify SCCs and their direct external parents, without regressing on all previously recovered variables. These characterizations yield BlockExo, which attains a structurally matching sample bound without knowing $s_{\max}$ or $d_B$ under suitable conditions. Simulations support the structural dependence of our sample bound and demonstrate BlockExo's sample-efficient recovery in comparisons with other methods for cyclic causal discovery.

Abstract: We introduce STRIDE (State-Transition Representation via Increment Dynamics and Evolution), which defines states through derivative fingerprints and learns local functions for state transitions (qpairs), recasting continuous forecasting as transition prediction. Trailing convolution windows estimate local joint-transition frequencies, whose lagged differences form a high-dimensional increment trajectory. Proper orthogonal decomposition (POD) gives coordinate paths, jointly forecast by sparse dynamics with memory. Recombining their forecasts and applying history-anchored inversion recovers future transition distributions; sampled state paths select local functions to generate continuous forecasts. Three-seed experiments compare STRIDE against fourteen baselines across nine benchmark families. Five independent Markov and hidden-state baselines cover all 230 evaluated tasks, with 220 complete whole-horizon pairs. Against these comparators, system-weighted late-Energy win fractions range from 73.6% to 78.5% on 190 multi-step pairs; against DLinear, the fraction is 77.3% on 72 paired multi-step tasks. Matched controls examine the intermediate representation. On 64 independently initialized Aizawa trajectories, late-Energy reductions against four matched controls range from approximately 24% to 56%, with all four prespecified contrasts passing Holm correction. These results connect transition-statistic prediction to continuous probabilistic forecasting, with substantial long-horizon gains in the matched Aizawa study.

Abstract: Neurosymbolic research typically assumes a pre-existing symbolic specification, leaving the upstream challenge of acquiring and formalizing requirements and constraints largely unaddressed. We present an architecture that fills this gap by using an OWL configuration ontology to mediate between neural constraint sources and downstream consumers. In this framework, LLM assistants elicit soft stakeholder preferences, while hardware specifications define hard physical and engineering limits. The ontology unifies these heterogeneous inputs, leverages description logic to identify unsatisfiability, and generates symbolic explanations that enable LLMs to interactively renegotiate terms with users. Any remaining conflicts are resolved downstream via priority-based relaxation. We illustrate our approach on a microgrid use case from the FLEXI project and argue its generalizability to multi-stakeholder domains where constraint acquisition is distributed across human and automated sources of unequal authority.

Abstract: Behavioural equivalences, such as language equivalence and probabilistic bisimilarity, are fundamental techniques for reducing the size of probabilistic models. However, these equivalences are sensitive to the precise values of transition probabilities, making them unsuitable in applications where probabilities are subject to approximation. Motivated by settings in which the support graph of a labelled Markov chain is known but the transition probabilities are uncertain, we study robust variants of these equivalences. We introduce universal (perturbation) equivalence, which captures a variant of equivalence that is resilient to all perturbations of transition probabilities: two states or distributions are universally equivalent if they remain equivalent under every assignment of transition probabilities consistent with the support graph. We also consider the dual notion of existential (perturbation) equivalence, which holds whenever there exists an assignment of transition probabilities that yields equivalence. We establish that, for states, universal language equivalence coincides with universal probabilistic bisimilarity and develop a characterisation that yields a polynomial-time partition refinement algorithm. We implement the algorithm and demonstrate experimentally that it is effective as a technique for robust model reduction. We further show that universal language equivalence for distributions is closely related to the state case, and prove NL-completeness of deciding universal equivalence for both states and distributions. We prove that, for states, existential language equivalence coincides with existential probabilistic bisimilarity and deterministic witness transition functions always suffice, leading to an NP-completeness result. In contrast, we show that existential language equivalence for distributions is complete for the existential theory of the reals.

Abstract: The development of generative artificial intelligence resources enables opportunities of speeding up systems and engineering design work. This contribution introduces a framework of formal operations for assembling context in LLM-based engineering design. This framework involves the assembly of modular context units, including policy prompts, reference units with persistence, and user questions with prompt vectoring. This approach enables the systematic structuring of interactions with generative models. A formal method for evaluating modelling-as-code LLM outputs is also presented, which enables the evaluation of compliance to intent from LLM answers and thereby asses the support from LLMs for systems architecture modelling.

Abstract: Modern science and engineering increasingly rely on time-varying data, yet the mathematical tools used to model temporal phenomena are often developed within separate disciplines, obscuring common principles and limiting the transfer of ideas across fields. This chapter presents the theory of narratives, an abstract framework for time-varying objects of any mathematical kind that supports both theoretical investigations and applications. To illustrate this perspective, the chapter develops three vignettes, each illustrating a different research direction. The first addresses a general concern: What information loss can occur when switching between different representations of temporal data? The second concerns structural and algorithmic approaches: How can we systematically decompose time-varying data into simple pieces and obtain invariants describing its structural complexity? The third is an application to control theory: How can we model multi-agent systems with switching communication topologies? More important than any individual vignette, the central message of this invitation is that a suitable abstract perspective can organize and guide research across remarkably diverse mathematical and scientific domains.