Bounded model checking of Time Petri Nets using SAT solver

Time Petri nets (TPN) are successfully used in the specification and analysis of distributed systems that involve explicit timing constraints. Especially, model checking TPN is a hopeful method for the formal verification of such complex systems. For this, it is promising to lean to the construction of an optimized version of the state space. The well-known methods of state space abstraction are SCG (state class graph) and ZBG (graph based on zones). For ZBG, a symbolic state represents the real evaluations of the clocks of the TPN; it is thus possible to directly check quantitative time properties. However, this method suffers from the state space explosion. To attenuate this problem, the authors propose in this paper to combine the ZBG approach with the partial order reduction technique based on stubborn set, leading thus to the proposal of a new state space abstraction called reduced zone-based graph (RZBG). The authors show via case studies the efficiency of the RZBG which is implemented and integrated within the 〖TPN-TCTL〗_h^∆ model checking in the model checker Romeo.

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Card-Based Cryptography Meets Formal Verification

New Generation Computing ◽

10.1007/s00354-020-00120-0 ◽

2021 ◽

Author(s):

Alexander Koch ◽

Michael Schrempp ◽

Michael Kirsten

Keyword(s):

Model Checking ◽

Formal Verification ◽

State Space ◽

Lower Bounds ◽

Bounded Model Checking ◽

Minimal Length ◽

State Spaces ◽

Bounded State ◽

Sat Solver ◽

General Translation

AbstractCard-based cryptography provides simple and practicable protocols for performing secure multi-party computation with just a deck of cards. For the sake of simplicity, this is often done using cards with only two symbols, e.g., $$\clubsuit $$ ♣ and $$\heartsuit $$ ♡ . Within this paper, we also target the setting where all cards carry distinct symbols, catering for use-cases with commonly available standard decks and a weaker indistinguishability assumption. As of yet, the literature provides for only three protocols and no proofs for non-trivial lower bounds on the number of cards. As such complex proofs (handling very large combinatorial state spaces) tend to be involved and error-prone, we propose using formal verification for finding protocols and proving lower bounds. In this paper, we employ the technique of software bounded model checking (SBMC), which reduces the problem to a bounded state space, which is automatically searched exhaustively using a SAT solver as a backend. Our contribution is threefold: (a) we identify two protocols for converting between different bit encodings with overlapping bases, and then show them to be card-minimal. This completes the picture of tight lower bounds on the number of cards with respect to runtime behavior and shuffle properties of conversion protocols. For computing AND, we show that there is no protocol with finite runtime using four cards with distinguishable symbols and fixed output encoding, and give a four-card protocol with an expected finite runtime using only random cuts. (b) We provide a general translation of proofs for lower bounds to a bounded model checking framework for automatically finding card- and run-minimal (i.e., the protocol has a run of minimal length) protocols and to give additional confidence in lower bounds. We apply this to validate our method and, as an example, confirm our new AND protocol to have its shortest run for protocols using this number of cards. (c) We extend our method to also handle the case of decks on symbols $$\clubsuit $$ ♣ and $$\heartsuit $$ ♡ , where we show run-minimality for two AND protocols from the literature.

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