Computer Science / Formal Languages and Automata Theory

All posts under category "Computer Science / Formal Languages and Automata Theory"

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Average-Based Robustness for Continuous-Time Signal Temporal Logic

Average-Based Robustness for Continuous-Time Signal Temporal Logic

We propose a new robustness score for continuous-time Signal Temporal Logic (STL) specifications. Instead of considering only the most severe point along the evolution of the signal, we use average scores to extract more information from the signal, emphasizing robust satisfaction of all the specifications subformulae over their entire time interval domains. We demonstrate the advantages of this new score in falsification and control synthesis problems in systems with complex dynamics and multi-agent systems.

paper research
VC Dimensions of Nondeterministic Finite Automata for Words of Equal Length

VC Dimensions of Nondeterministic Finite Automata for Words of Equal Length

Let $NFA_b(q)$ denote the set of languages accepted by nondeterministic finite automata with $q$ states over an alphabet with $b$ letters. Let $B_n$ denote the set of words of length $n$. We give a quadratic lower bound on the VC dimension of [ NFA_2(q) cap B_n = {L cap B_n mid L in NFA_2(q) } ] as a function of $q$. Next, the work of Gruber and Holzer (2007) gives an upper bound for the nondeterministic state complexity of finite languages contained in $B_n$, which we strengthen using our methods. Finally, we give some theoretical and experimental results on the dependence on $n$ of the VC dimension and testing dimension of $NFA_2(q) cap B_n$.

paper research

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