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1. Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications.

   Bansal, Suguman ( April 2020 , Proceedings of the AAAI Conference on Artificial Intelligence)

   LTLf synthesis is the automated construction of a reactive system from a high-level description, expressed in LTLf, of its finite-horizon behavior. So far, the conversion of LTLf formulas to deterministic finite-state automata (DFAs) has been identified as the primary bottleneck to the scalabity of synthesis. Recent investigations have also shown that the size of the DFA state space plays a critical role in synthesis as well. Therefore, effective resolution of the bottleneck for synthesis requires the conversion to be time and memory performant, and prevent state-space explosion. Current conversion approaches, however, which are based either on explicit-state representation or symbolic-state representation, fail to address these necessities adequately at scale: Explicit-state approaches generate minimal DFA but are slow due to expensive DFA minimization. Symbolic-state representations can be succinct, but due to the lack of DFA minimization they generate such large state spaces that even their symbolic representations cannot compensate for the blow-up. This work proposes a hybrid representation approach for the conversion. Our approach utilizes both explicit and symbolic representations of the state-space, and effectively leverages their complementary strengths. In doing so, we offer an LTLf to DFA conversion technique that addresses all three necessities, hence resolving the bottleneck. A comprehensive empirical evaluation on conversion and synthesis benchmarks supports the merits of our hybrid approach. 

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2. Partitioning Techniques in LTLf Synthesis

   Tabajara, Lucas M ; Vardi, Moshe Y ( July 2019 , 2019 International Joint Conference on Artificial Intelligence)

   Decomposition is a general principle in computational thinking, aiming at decomposing a problem instance into easier subproblems. Indeed, decomposing a transition system into a partitioned transition relation was critical to scaling BDD-based model checking to large state spaces. Since then, it has become a standard technique for dealing with related problems, such as Boolean synthesis. More recently, partitioning has begun to be explored in the synthesis of reactive systems. LTLf synthesis, a finite-horizon version of reactive synthesis with applications in areas such as robotics, seems like a promising candidate for partitioning techniques. After all, the state of the art is based on a BDD-based symbolic algorithm similar to those from model checking, and partitioning could be a potential solution to the current bottleneck of this approach, which is the construction of the state space. In this work, however, we expose fundamental limitations of partitioning that hinder its effective application to symbolic LTLf synthesis. We not only provide evidence for this fact through an extensive experimental evaluation, but also perform an in depth analysis to identify the reason for these results. We trace the issue to an overall increase in the size of the explored state space, caused by an inability of partitioning to fully exploit state-space minimization, which has a crucial effect on performance. We conclude that more specialized decomposition techniques are needed for LTLf synthesis which take into account the effects of minimization. 

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3. LTLf Synthesis as AND-OR Graph Search: Knowledge Compilation at Work

   https://doi.org/10.24963/ijcai.2022/359  

   De Giacomo, Giuseppe ; Favorito, Marco ; Li, Jianwen ; Vardi, Moshe Y. ; Xiao, Shengping ; Zhu, Shufang ( July 2022 , IJCAI)

   Synthesis techniques for temporal logic specifications are typically based on exploiting symbolic techniques, as done in model checking. These symbolic techniques typically use backward fixpoint computation. Planning, which can be seen as a specific form of synthesis, is a witness of the success of forward search approaches. In this paper, we develop a forward-search approach to full-fledged Linear Temporal Logic on finite traces (LTLf) synthesis. We show how to compute the Deterministic Finite Automaton (DFA) of an LTLf formula on-the-fly, while performing an adversarial forward search towards the final states, by considering the DFA as a sort of AND-OR graph. Our approach is characterized by branching on suitable propositional formulas, instead of individual evaluations, hence radically reducing the branching factor of the search space. Specifically, we take advantage of techniques developed for knowledge compilation, such as Sentential Decision Diagrams (SDDs), to implement the approach efficiently.

    

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4. Imitation-Projected Programmatic Reinforcement Learning

   Verma, A ( December 2019 , Advances in neural information processing systems)

   Wallach, H (Ed.)

   We study the problem of programmatic reinforcement learning, in which policies are represented as short programs in a symbolic language. Programmatic policies can be more interpretable, generalizable, and amenable to formal verification than neural policies; however, designing rigorous learning approaches for such policies remains a challenge. Our approach to this challenge-a meta-algorithm called PROPEL-is based on three insights. First, we view our learning task as optimization in policy space, modulo the constraint that the desired policy has a programmatic representation, and solve this optimization problem using a form of mirror descent that takes a gradient step into the unconstrained policy space and then projects back onto the constrained space. Second, we view the unconstrained policy space as mixing neural and programmatic representations, which enables employing state-of-the-art deep policy gradient approaches. Third, we cast the projection step as program synthesis via imitation learning, and exploit contemporary combinatorial methods for this task. We present theoretical convergence results for PROPEL and empirically evaluate the approach in three continuous control domains. The experiments show that PROPEL can significantly outperform state-of-the-art approaches for learning programmatic policies. 

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5. A Symbolic Approach to Detecting Hardware Trojans Triggered by Don’t Care Transitions

   https://doi.org/10.1145/3558392  

   Dai, Ruochen ; Yavuz, Tuba ( March 2023 , ACM Transactions on Design Automation of Electronic Systems)

   Due to the globalization of Integrated Circuit supply chain, hardware Trojans and the attacks that can trigger them have become an important security issue. One type of hardware Trojans leverages the “don’t care transitions” in Finite-state Machines (FSMs) of hardware designs. In this article, we present a symbolic approach to detecting don’t care transitions and the hidden Trojans. Our detection approach works at both register-transfer level (RTL) and gate level, does not require a golden design, and works in three stages. In the first stage, it explores the reachable states. In the second stage, it performs an approximate analysis to find the don’t care transitions and any discrepancies in the register values or output lines due to don’t care transitions. The second stage can be used for both predicting don’t care triggered Trojans and for guiding don’t care aware reachability analysis. In the third stage, it performs a state-space exploration from reachable states that have incoming don’t care transitions to explore the Trojan payload and to find behavioral discrepancies with respect to what has been observed in the first stage. We also present a pruning technique based on the reachability of FSM states. We present a methodology that leverages both RTL and gate-level for soundness and efficiency. Specifically, we show that don’t care transitions and Trojans that leverage them must be detected at the gate-level, i.e., after synthesis has been performed, for soundness. However, under specific conditions, Trojan payload exploration can be performed more efficiently at RTL. Additionally, the modular design of our approach also provides a fast Trojan prediction method even at the gate level when the reachable states of the FSM is known a priori . Evaluation of our approach on a set of benchmarks from OpenCores and TrustHub and using gate-level representation generated by two synthesis tools, YOSYS and Synopsis Design Compiler (SDC), shows that our approach is both efficient (up to 10× speedup w.r.t. no pruning) and precise (0% false positives both at RTL and gate-level netlist) in detecting don’t care transitions and the Trojans that leverage them. Additionally, the total analysis time can achieve up to 1.62× (using YOSYS) and 1.92× (using SDC) speedup when synthesis preserves the FSM structure, the foundry is trusted, and the Trojan detection is performed at RTL. 

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