arXiv subjects

Dana Fisman

Publications and source records attributed to Dana Fisman.

At least 19 recordsLinked to original sources

arXiv2026

Asymptotic Hausdorff and Language Similarity

We introduce the \textit{Asymptotic Hausdorff} lifting, denoted $\mathbb{AH}_{d}$, a general method for lifting an element-level metric $d$ to a (pseudo-) metric on sets, that captures asymptotic similarity in infinite domains equipped with a notion of size. The construction is designed to be insensitive to finite deviations and to avoid the limitations of classical Hausdorff-based approaches, which are often overly sensitive to outliers and fail to reflect asymptotic behavior. Formal languages provide a central motivating instance of this framework, where elements are words and sets are languages. When applied to normalized edit distances, the Asymptotic Hausdorff lifting yields metric-valued distances between languages that reflect asymptotic edit behavior while preserving metric structure. We study the equivalence classes of regular languages induced by $\mathbb{AH}_{d}$ for normalized edit distances $d$, and characterize their asymptotic essence. Focusing in particular on the normalized edit distance of Marzal and Vidal, $\textsf{ned}$, we investigate the computation of $\mathbb{AH}_{\textsf{ned}}$ for regular languages and for bounded context-free languages.

cs.FL↗

arXiv2026

Characterizing LTL Formulas by Examples (full version)

We investigate the extent to which Linear Temporal Logic (LTL) formulas can be uniquely characterized by a finite set of labeled examples. We consider different types of examples, ranging from finite words to transfinite words, as well as schematic examples. In the finite-word setting, we provide a complete classification of basis-restricted LTL fragments that admit such unique characterizations. Next, we show that allowing transfinite words as examples enables finite unique characterizations for large monotone fragments of LTL. Finally, we introduce schematic examples, i.e., patterns that compactly represent a family of finite words, and we show that these enable unique characterization results in the finite setting that were not possible with ordinary finite examples alone. Overall, the work provides a foundational account of the descriptive power of different example types for example-driven specification, debugging, and learning of temporal properties.

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arXiv2025

Atomic Gliders and CA as Language Generators (Extended Version)

Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a formal treatment of CA as genuine language generators remains underdeveloped. We formalize CA-expressible languages as sets of finite words obtained by projecting the non-quiescent segments of configurations reachable by one-dimensional, deterministic, synchronous CA over bi-infinite grids. These languages are defined with respect to sets of initial configurations specified by a regular language as in regular model checking. To capture structured dynamics, we propose a glider-based generative semantics for CA. Inspired by the classical notion of gliders, we define a glider as a one-cell entity carrying a symbol in a certain velocity under well defined interaction semantics. We show that despite the regularity of the initial configurations and the locality of the transition rules, the resulting languages can exhibit non-regular and even non-context-free structure. This positions regular-initialized CA languages as a surprisingly rich computational model, with potential applications in the formal analysis of linearly ordered MAS.

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arXiv2025

Runtime Consultants

In this paper we introduce the notion of a runtime consultant. A runtime consultant is defined with respect to some value function on infinite words. Similar to a runtime monitor, it runs in parallel to an execution of the system and provides inputs at every step of the run. While a runtime monitor alerts when a violation occurs, the idea behind a consultant is to be pro-active and provide recommendations for which action to take next in order to avoid violation (or obtain a maximal value for quantitative objectives). It is assumed that a runtime-controller can take these recommendations into consideration. The runtime consultant does not assume that its recommendations are always followed. Instead, it adjusts to the actions actually taken (similar to a vehicle navigation system). We show how to compute a runtime consultant for common value functions used in verification, and that almost all have a runtime consultant that works in constant time. We also develop consultants for $ω$-regular properties, under both their classical Boolean semantics and their recently proposed quantitative interpretation.

cs.FL↗

arXiv2025

Omega-Regular Robustness

Roughly speaking, a system is said to be robust if it can resist disturbances and still function correctly. For instance, if the requirement is that the temperature remains in an allowed range $[l,h]$, then a system that remains in a range $[l',h']\subset[l,h]$ is more robust than one that reaches $l$ and $h$ from time to time. In this example the initial specification is quantitative in nature, this is not the case in $ω$-regular properties. Still, it seems there is a natural robustness preference relation induced by an $ω$-regular property. E.g. for a property requiring that every request is eventually granted, one would say that a system where requests are granted two ticks after they are issued is more robust than one in which requests are answered ninety ticks after they are issued. In this work we manage to distill a robustness preference relation that is induced by a given $ω$-regular language. The robustness preference relation is a semantic notion (agnostic to the given representation of the language) that relies on Wagner's hierarchy and on Ehlers and Schewe's definition of natural rank of infinite words. It aligns with our intuitions on common examples, satisfies some natural mathematical criteria, and refines Tabuada and Neider's five-valued semantics into an infinite domain.

cs.FL↗

arXiv2024

Constructing Concise Characteristic Samples for Acceptors of Omega Regular Languages

A characteristic sample for a language $L$ and a learning algorithm $\textbf{L}$ is a finite sample of words $T_L$ labeled by their membership in $L$ such that for any sample $T \supseteq T_L$ consistent with $L$, on input $T$ the learning algorithm $\textbf{L}$ returns a hypothesis equivalent to $L$. Which omega automata have characteristic sets of polynomial size, and can these sets be constructed in polynomial time? We address these questions here. In brief, non-deterministic omega automata of any of the common types, in particular Büchi, do not have characteristic samples of polynomial size. For deterministic omega automata that are isomorphic to their right congruence automata, the fully informative languages, polynomial time algorithms for constructing characteristic samples and learning from them are given. The algorithms for constructing characteristic sets in polynomial time for the different omega automata (of types Büchi, coBüchi, parity, Rabin, Street, or Muller), require deterministic polynomial time algorithms for (1) equivalence of the respective omega automata, and (2) testing membership of the language of the automaton in the informative classes, which we provide.

cs.FL↗

arXiv2024

A Robust Measure on FDFAs Following Duo-Normalized Acceptance

Families of DFAs (FDFAs) are a computational model recognizing $ω$-regular languages. They were introduced in the quest of finding a Myhill-Nerode theorem for $ω$-regular languages, and obtaining learning algorithms. FDFAs have been shown to have good qualities in terms of the resources required for computing Boolean operations on them (complementation, union, and intersection) and answering decision problems (emptiness and equivalence); all can be done in non-deterministic logspace. In this paper we study FDFAs with a new type of acceptance condition, duo-normalization, that generalizes the traditional normalization acceptance type. We show that duo-normalized FDFAs are advantageous to normalized FDFAs in terms of succinctness as they can be exponentially smaller. Fortunately this added succinctness doesn't come at the cost of increasing the complexity of Boolean operations and decision problems -- they can still be preformed in non-deterministic logspace. An important measure of the complexity of an $ω$-regular language, is its position in the Wagner hierarchy. It is based on the inclusion measure of Muller automata and for the common $ω$-automata there exist algorithms computing their position. We develop a similarly robust measure for duo-normalized (and normalized) FDFAs, which we term the diameter measure. We show that the diameter measure corresponds one-to-one to the position on the Wagner hierarchy. We show that computing it for duo-normalized FDFAs is PSPACE-complete, while it can be done in non-deterministic logspace for traditional FDFAs.

cs.FL↗

arXiv2023

Learning Broadcast Protocols

The problem of learning a computational model from examples has been receiving growing attention. For the particularly challenging problem of learning models of distributed systems, existing results are restricted to models with a fixed number of interacting processes. In this work we look for the first time (to the best of our knowledge) at the problem of learning a distributed system with an arbitrary number of processes, assuming only that there exists a cutoff, i.e., a number of processes that is sufficient to produce all observable behaviors. Specifically, we consider fine broadcast protocols, these are broadcast protocols (BPs) with a finite cutoff and no hidden states. We provide a learning algorithm that can infer a correct BP from a sample that is consistent with a fine BP, and a minimal equivalent BP if the sample is sufficiently complete. On the negative side we show that (a) characteristic sets of exponential size are unavoidable, (b) the consistency problem for fine BPs is NP hard, and (c) that fine BPs are not polynomially predictable.

cs.FL↗

arXiv2023

Inferring Symbolic Automata

We study the learnability of symbolic finite state automata (SFA), a model shown useful in many applications in software verification. The state-of-the-art literature on this topic follows the query learning paradigm, and so far all obtained results are positive. We provide a necessary condition for efficient learnability of SFAs in this paradigm, from which we obtain the first negative result. The main focus of our work lies in the learnability of SFAs under the paradigm of identification in the limit using polynomial time and data, and its strengthening efficient identifiability, which are concerned with the existence of a systematic set of characteristic samples from which a learner can correctly infer the target language. We provide a necessary condition for identification of SFAs in the limit using polynomial time and data, and a sufficient condition for efficient learnability of SFAs. From these conditions we derive a positive and a negative result. The performance of a learning algorithm is typically bounded as a function of the size of the representation of the target language. Since SFAs, in general, do not have a canonical form, and there are trade-offs between the complexity of the predicates on the transitions and the number of transitions, we start by defining size measures for SFAs. We revisit the complexity of procedures on SFAs and analyze them according to these measures, paying attention to the special forms of SFAs: normalized SFAs and neat SFAs, as well as to SFAs over a monotonic effective Boolean algebra. This is an extended version of the paper with the same title published in CSL'22.

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arXiv2023

Learning of Structurally Unambiguous Probabilistic Grammars

The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness results for learning context-free grammars in general, and probabilistic grammars in particular, most of the literature has concentrated on the second problem. In this work we address the first problem. We restrict attention to structurally unambiguous weighted context-free grammars (SUWCFG) and provide a query learning algorithm for \structurally unambiguous probabilistic context-free grammars (SUPCFG). We show that SUWCFG can be represented using \emph{co-linear multiplicity tree automata} (CMTA), and provide a polynomial learning algorithm that learns CMTAs. We show that the learned CMTA can be converted into a probabilistic grammar, thus providing a complete algorithm for learning a structurally unambiguous probabilistic context free grammar (both the grammar topology and the probabilistic weights) using structured membership queries and structured equivalence queries. A summarized version of this work was published at AAAI 21.

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arXiv2022

The Normalized Edit Distance with Uniform Operation Costs is a Metric

We prove that the normalized edit distance proposed in [Marzal and Vidal 1993] is a metric when the cost of all the edit operations are the same. This closes a long standing gap in the literature where several authors noted that this distance does not satisfy the triangle inequality in the general case, and that it was not known whether it is satisfied in the uniform case where all the edit costs are equal. We compare this metric to two normalized metrics proposed as alternatives in the literature, when people thought that Marzal's and Vidal's distance is not a metric, and identify key properties that explain why the original distance, now known to also be a metric, is better for some applications. Our examination is from a point of view of formal verification, but the properties and their significance are stated in an application agnostic way.

cs.FL↗

arXiv2021

On the Complexity of Symbolic Finite-State Automata

We revisit the complexity of procedures on SFAs (such as intersection, emptiness, etc.) and analyze them according to the measures we find suitable for symbolic automata: the number of states, the maximal number of transitions exiting a state, and the size of the most complex transition predicate. We pay attention to the special forms of SFAs: {normalized SFAs} and {neat SFAs}, as well as to SFAs over a {monotonic} effective Boolean algebra.

cs.FL↗

arXiv2021

Learning of Structurally Unambiguous Probabilistic Grammars

The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness results for learning context-free grammars in general, and probabilistic grammars in particular, most of the literature has concentrated on the second problem. In this work we address the first problem. We restrict attention to structurally unambiguous weighted context-free grammars (SUWCFG) and provide a query learning algorithm for structurally unambiguous probabilistic context-free grammars (SUPCFG). We show that SUWCFG can be represented using co-linear multiplicity tree automata (CMTA), and provide a polynomial learning algorithm that learns CMTAs. We show that the learned CMTA can be converted into a probabilistic grammar, thus providing a complete algorithm for learning a structurally unambiguous probabilistic context free grammar (both the grammar topology and the probabilistic weights) using structured membership queries and structured equivalence queries. We demonstrate the usefulness of our algorithm in learning PCFGs over genomic data.

cs.FL↗

arXiv2020

Safety Synthesis Sans Specification

We define the problem of learning a transducer ${S}$ from a target language $U$ containing possibly conflicting transducers, using membership queries and conjecture queries. The requirement is that the language of ${S}$ be a subset of $U$. We argue that this is a natural question in many situations in hardware and software verification. We devise a learning algorithm for this problem and show that its time and query complexity is polynomial with respect to the rank of the target language, its incompatibility measure, and the maximal length of a given counterexample. We report on experiments conducted with a prototype implementation.

cs.FL↗

arXiv2020

Polynomial time algorithms for inclusion and equivalence of deterministic omega acceptors

The class of omega languages recognized by deterministic parity acceptors (DPAs) or deterministic Muller acceptors (DMAs) is exactly the regular omega languages. The inclusion problem is the following: given two acceptors A1 and A2, determine whether the language recognized by A1 is a subset of the language recognized by A2, and if not, return an ultimately periodic omega word accepted by A1 but not A2. We describe polynomial time algorithms to solve this problem for two DPAs and for two DMAs. Corollaries include polynomial time algorithms to solve the equivalence problem for DPAs and DMAs, and also the inclusion and equivalence problems for deterministic Buechi and coBuechi acceptors.

cs.FL↗

arXiv2020

Learning Interpretable Models in the Property Specification Language

We address the problem of learning human-interpretable descriptions of a complex system from a finite set of positive and negative examples of its behavior. In contrast to most of the recent work in this area, which focuses on descriptions expressed in Linear Temporal Logic (LTL), we develop a learning algorithm for formulas in the IEEE standard temporal logic PSL (Property Specification Language). Our work is motivated by the fact that many natural properties, such as an event happening at every n-th point in time, cannot be expressed in LTL, whereas it is easy to express such properties in PSL. Moreover, formulas in PSL can be more succinct and easier to interpret (due to the use of regular expressions in PSL formulas) than formulas in LTL. Our learning algorithm builds on top of an existing algorithm for learning LTL formulas. Roughly speaking, our algorithm reduces the learning task to a constraint satisfaction problem in propositional logic and then uses a SAT solver to search for a solution in an incremental fashion. We have implemented our algorithm and performed a comparative study between the proposed method and the existing LTL learning algorithm. Our results illustrate the effectiveness of the proposed approach to provide succinct human-interpretable descriptions from examples.

cs.LG↗

arXiv2019

Streamable Regular Transductions

Motivated by real-time monitoring and data processing applications, we develop a formal theory of quantitative queries for streaming data that can be evaluated efficiently. We consider the model of unambiguous Cost Register Automata (CRAs), which are machines that combine finite-state control (for identifying regular patterns) with a finite set of data registers (for computing numerical aggregates). The definition of CRAs is parameterized by the collection of numerical operations that can be applied to the registers. These machines give rise to the class of streamable regular transductions (SR), and to the class of streamable linear regular transductions (SLR) when the register updates are copyless, i.e. every register appears at most once the right-hand-side expressions of the updates. We give a logical characterization of the class SR (resp., SLR) using MSO-definable transformations from strings to DAGs (resp., trees) without backward edges. Additionally, we establish that the two classes SR and SLR are closed under operations that are relevant for designing query languages. Finally, we study the relationship with weighted automata (WA), and show that CRAs over a suitably chosen set of operations correspond to WA, thus establishing that WA are a special case of CRAs.

cs.FL↗

arXiv2019

Query learning of derived $ω$-tree languages in polynomial time

We present the first polynomial time algorithm to learn nontrivial classes of languages of infinite trees. Specifically, our algorithm uses membership and equivalence queries to learn classes of $ω$-tree languages derived from weak regular $ω$-word languages in polynomial time. The method is a general polynomial time reduction of learning a class of derived $ω$-tree languages to learning the underlying class of $ω$-word languages, for any class of $ω$-word languages recognized by a deterministic Büchi acceptor. Our reduction, combined with the polynomial time learning algorithm of Maler and Pnueli [1995] for the class of weak regular $ω$-word languages yields the main result. We also show that subset queries that return counterexamples can be implemented in polynomial time using subset queries that return no counterexamples for deterministic or non-deterministic finite word acceptors, and deterministic or non-deterministic Büchi $ω$-word acceptors. A previous claim of an algorithm to learn regular $ω$-trees due to Jayasrirani, Begam and Thomas [2008] is unfortunately incorrect, as shown in Angluin [2016].

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