Formal Languages and Automata Theory

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href=/list/cs.FL/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> <dl id='articles'> <h3>Cross submissions (showing 1 of 1 entries)</h3> <dt> <a name='item1'>[1]</a> <a href ="/abs/2503.13660" title="Abstract" id="2503.13660"> arXiv:2503.13660 </a> (cross-list from cs.RO) [<a href="/pdf/2503.13660" title="Download PDF" id="pdf-2503.13660" aria-labelledby="pdf-2503.13660">pdf</a>, <a href="https://arxiv.org/html/2503.13660v1" title="View HTML" id="html-2503.13660" aria-labelledby="html-2503.13660" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.13660" title="Other formats" id="oth-2503.13660" aria-labelledby="oth-2503.13660">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> INPROVF: Leveraging Large Language Models to Repair High-level Robot Controllers from Assumption Violations </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Meng,+Q">Qian Meng</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Zhou,+J+P">Jin Peng Zhou</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Weinberger,+K+Q">Kilian Q. Weinberger</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Kress-Gazit,+H">Hadas Kress-Gazit</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> To appear in ICLR 2025 Workshop: VerifAI: AI Verification in the Wild; in submission to 2025 IEEE 21th International Conference on Automation Science and Engineering (CASE), Los Angeles, CA, USA: IEEE, Aug. 2025 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Robotics (cs.RO)</span>; Artificial Intelligence (cs.AI); Formal Languages and Automata Theory (cs.FL) </div> <p class='mathjax'> This paper presents INPROVF, an automatic framework that combines large language models (LLMs) and formal methods to speed up the repair process of high-level robot controllers. Previous approaches based solely on formal methods are computationally expensive and cannot scale to large state spaces. In contrast, INPROVF uses LLMs to generate repair candidates, and formal methods to verify their correctness. To improve the quality of these candidates, our framework first translates the symbolic representations of the environment and controllers into natural language descriptions. If a candidate fails the verification, INPROVF provides feedback on potential unsafe behaviors or unsatisfied tasks, and iteratively prompts LLMs to generate improved solutions. We demonstrate the effectiveness of INPROVF through 12 violations with various workspaces, tasks, and state space sizes. </p> </div> </dd> </dl> <dl id='articles'> <h3>Replacement submissions (showing 2 of 2 entries)</h3> <dt> <a name='item2'>[2]</a> <a href ="/abs/2407.09891" title="Abstract" id="2407.09891"> arXiv:2407.09891 </a> (replaced) [<a href="/pdf/2407.09891" title="Download PDF" id="pdf-2407.09891" aria-labelledby="pdf-2407.09891">pdf</a>, <a href="https://arxiv.org/html/2407.09891v3" title="View HTML" id="html-2407.09891" aria-labelledby="html-2407.09891" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.09891" title="Other formats" id="oth-2407.09891" aria-labelledby="oth-2407.09891">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Blow-up in Non-Deterministic Automata </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Baburin,+I">Ivan Baburin</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Cotterell,+R">Ryan Cotterell</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Formal Languages and Automata Theory (cs.FL)</span> </div> <p class='mathjax'> In this paper we examine the difficulty of finding an equivalent deterministic automaton when confronted with a non-deterministic one. While for some automata the exponential blow-up in their number of states is unavoidable, we show that in general, any approximation of state complexity with polynomial precision remains PSPACE-hard. The same is true when using the subset construction to determinize the NFA, meaning that it is PSPACE-hard to predict whether subset construction will produce an exponential ''blow-up'' in the number of states or not. To give an explanation for its behaviour, we propose the notion of subset complexity, which serves as an upper bound on the size of subset construction. Due to it simple and intuitive nature it allows to identify large classes of automata which can have limited non-determinism and completely avoid the ''blow-up''. Subset complexity also remains invariant under NFA reversal and allows to predict how the introduction or removal of transitions from the NFA will affect its size. </p> </div> </dd> <dt> <a name='item3'>[3]</a> <a href ="/abs/2411.12537" title="Abstract" id="2411.12537"> arXiv:2411.12537 </a> (replaced) [<a href="/pdf/2411.12537" title="Download PDF" id="pdf-2411.12537" aria-labelledby="pdf-2411.12537">pdf</a>, <a href="https://arxiv.org/html/2411.12537v5" title="View HTML" id="html-2411.12537" aria-labelledby="html-2411.12537" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.12537" title="Other formats" id="oth-2411.12537" aria-labelledby="oth-2411.12537">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Unlocking State-Tracking in Linear RNNs Through Negative Eigenvalues </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Grazzi,+R">Riccardo Grazzi</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Siems,+J">Julien Siems</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Zela,+A">Arber Zela</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Franke,+J+K">J枚rg K.H. Franke</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Hutter,+F">Frank Hutter</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Pontil,+M">Massimiliano Pontil</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> V2: Correction to Theorem 1 and 2 and to point 3 of Proposition 1. V3: ICLR Camera Ready, V4: ICLR Camera Ready, added figures to theory section, updated modular arithmetic with brackets results because previous results did not contain multiplication </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (cs.LG)</span>; Computation and Language (cs.CL); Formal Languages and Automata Theory (cs.FL) </div> <p class='mathjax'> Linear Recurrent Neural Networks (LRNNs) such as Mamba, RWKV, GLA, mLSTM, and DeltaNet have emerged as efficient alternatives to Transformers for long sequences. However, both Transformers and LRNNs struggle to perform state-tracking, which may impair performance in tasks such as code evaluation. In one forward pass, current architectures are unable to solve even parity, the simplest state-tracking task, which non-linear RNNs can handle effectively. Recently, Sarrof et al. (2024) demonstrated that the failure of LRNNs like Mamba to solve parity stems from restricting the value range of their diagonal state-transition matrices to $[0, 1]$ and that incorporating negative values can resolve this issue. We extend this result to non-diagonal LRNNs such as DeltaNet. We prove that finite precision LRNNs with state-transition matrices having only positive eigenvalues cannot solve parity, while non-triangular matrices are needed to count modulo $3$. Notably, we also prove that LRNNs can learn any regular language when their state-transition matrices are products of identity minus vector outer product matrices, each with eigenvalues in the range $[-1, 1]$. Our experiments confirm that extending the eigenvalue range of Mamba and DeltaNet to include negative values not only enables them to solve parity but consistently improves their performance on state-tracking tasks. We also show that state-tracking enabled LRNNs can be pretrained stably and efficiently at scale (1.3B parameters), achieving competitive performance on language modeling and showing promise on code and math tasks. </p> </div> </dd> </dl> <div class='paging'>Total of 3 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/cs.FL/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> </div> </div> </div> </main> <footer style="clear: both;"> <div class="columns is-desktop" role="navigation" aria-label="Secondary" style="margin: -0.75em -0.75em 0.75em -0.75em">  <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; 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Formal Languages and Automata Theory