Table of Contents

• About
• Installation
  • Install prerequisites for RTAMT installation
  • Option 1: Install Python package version
  • Option 2: Build the tool
    • Clone the repository
    • Build CPP libraries
    • Install RTAMT
    • uninstall RTAMT
  • test RTAMT
• Theory
  • Specification Language
• Usage
  • Example Usage
    • Discrete-time online monitor
    • Dense-time online monitor
  • Dense-time Offline Monitor
  • Discrete-time Specifics
    • Working with time units and timing assumptions
• References

About

RTAMT is a Python (2- and 3-compatible) library for monitoring of Signal Temporal Logic (STL). The library implements algorithms offline and online monitoring of discrete-time and dense-time STL. The online monitors support the bounded future fragment of STL. The online discrete-time part of the library has an optimized C++ back-end.

Installation

Install prerequisites for RTAMT installation

sudo apt install libboost-all-dev
sudo apt install python-dev
sudo apt install python-pip

If your want to extend the specification language, you may need the ANTLR4 parser generator.

sudo apt install antlr4

You will also need CMake version 3.12 or higher if you need to build the CPP backend.

sudo apt install cmake

In our experience, Ubuntu 16.04, 18.04 don't support the versions in default. You can check our manual installation of cmake.

Option 1: Install Python package version

We provide Python package version of RTAMT.

for Python 2

sudo pip2 install rtamt

for Python 3

sudo pip3 install rtamt

Option 2: Build the tool

Clone the repository

git clone https://github.com/nickovic/rtamt

Build CPP libraries

This step is needed only if you want to use the CPP backend and can be skipped if you want to use pure Python monitors.

for Python 2

cd rtamt/rtamt
mkdir build
cd build
cmake -DPythonVersion=2 ../
make

for Python 3

cd rtamt/rtamt
mkdir build
cd build
cmake -DPythonVersion=3 ../
make

Install RTAMT

for Python 2

cd rtamt/
sudo pip2 install .

for Python 3

cd rtamt/
sudo pip3 install .

uninstall RTAMT

for Python 2

sudo pip2 uninstall rtamt

for Python 3

sudo pip3 uninstall rtamt

test RTAMT

for Python 2

cd rtamt/
python2 -m unittest discover tests/

for Python 3

cd rtamt/
python3 -m unittest discover tests/

Theory

RTAMT is a Python library for offline and online monitoring of (bounded-future)
Signal Temporal Logic (STL). The library is inspired by several theoretical and practical
works:

• The bounded-future fragment of STL is inspired by [3]
• The interface-aware interpretation of STL quantitative semantics is inspired by [4]
• The periodic-sampling interpretation of specifications (even in presence of timestamps that are not perfectly periodic) is inspired by [5]
• The translation of bounded-future STL to "equirobust" past STL prior to the online monitoring phase is inspired by [3]

Specification Language

RTAMT supports Signal Temporal Logic (STL) and interface-aware STL (IA-STL).

The library supports a variant of STL with past and future temporal operators as well as basic arithmetic and absolute value operators.
Semantics of STL is defined in terms of a robustness degree rho(phi,w,t), a function defined over real numbers extended with +inf and -inf that takes as input an STL specification phi, an input signal w and time index t, and computes how far is the signal w at time t from satisfying/violating phi. The robustness degree function is defined inductively as follows (c is a real constant, x is a variable, w_x(t) denotes the value of w projected to x at time t, a,b are rational constants such that 0 <= a <= b and |w| is the length of w):

% Constant
rho(c,w,t) = c

% Variable
rho(x,w,t) = w_x(t)

% Absolute value, exponentials
rho(abs(phi),w,t) = |rho(phi,w,t)|
rho(exp(phi),w,t) = e**rho(phi,w,t)
rho(pow(phi1, phi2),w,t) = rho(phi1,w,t)**rho(phi2,w,t)

% Arithmetic operators
rho(phi + psi,w,t) = rho(phi,w,t) + rho(psi,w,t)
rho(phi - psi,w,t) = rho(phi,w,t) - rho(psi,w,t)
rho(phi * psi,w,t) = rho(phi,w,t) * rho(psi,w,t)
rho(phi / psi,w,t) = rho(phi,w,t) / rho(psi,w,t)

% Numeric predicates
rho(phi <= psi,w,t) = rho(psi,w,t) - rho(phi,w,t) 
rho(phi < psi,w,t) = rho(psi,w,t) - rho(phi,w,t)
rho(phi >= psi,w,t) = rho(phi,w,t) - rho(psi,w,t)
rho(phi > psi,w,t) = rho(phi,w,t) - rho(psi,w,t)
rho(phi == psi,w,t) = -|rho(phi,w,t) - rho(psi,w,t)|
rho(phi !== psi,w,t) = |rho(phi,w,t) - rho(psi,w,t)|

% Boolean operators
rho(not(phi),w,t) = -rho(phi,w,t)
rho(phi or psi,w,t) = max(rho(phi,w,t),rho(psi,w,t))
rho(phi and psi,w,t) = min(rho(phi,w,t),rho(psi,w,t))
rho(phi -> psi,w,t) = max(-rho(phi,w,t),rho(psi,w,t))
rho(phi <-> psi,w,t) = -|rho(phi,w,t) - rho(psi,w,t)|
rho(phi xor psi,w,t) = |rho(phi,w,t) - rho(psi,w,t)|

% Events
rho(rise(phi),w,t) = rho(phi,w,t)                     if t=0
                     min(-rho(phi,w,t-1),rho(phi,w,t) otherwise
rho(fall(phi),w,t) = -rho(phi,w,t)                    if t=0
                     min(rho(phi,w,t-1),-rho(phi,w,t) otherwise

% Past untimed temporal operators
rho(prev phi,w,t) = -inf            if t<=0
                    rho(phi,w,t-1) otherwise
rho(once phi,w,t) = max_{t' in [0,t]} rho(phi,w,t')
rho(historically phi,w,t) = min_{t' in [0,t]} rho(phi,w,t')
rho(phi since psi,w,t) = max_{t' in [0,t]}(min(rho(psi,w,t'), min_{t'' in (t',t]} rho(phi,w,t'')))

% Past timed temporal operators
rho(once[a,b] phi,w,t) = -inf                                                            if t-a < 0
                         max_{t' in ([0,t] intersect [t-a,t-b])} rho(phi,w,t')           otherwise
rho(historically[a,b] phi,w,t) = inf                                                     if t-a < 0
                                 min_{t' in ([0,t] intersect [t-a,t-b])} rho(phi,w,t')   otherwise
rho(phi since[a,b] psi,w,t) = -inf                                                       if t-a < 0 
                              max_{t' in ([0,t] intersect [t-a,t-b]} (min(rho(psi,w,t'), 
                              min_{t'' in (t',t]} rho(phi,w,t'')))          otherwise

% Future untimed temporal operators
rho(next phi,w,t) = rho(phi,w,t+1)
rho(eventually phi,w,t) = max_{t' in [t,|w|]} rho(phi,w,t')
rho(always phi,w,t) = min_{t' in [t, |w|]} rho(phi,w,t')
rho(phi until psi,w,t) = max_{t' in [t,|w|] min(rho(psi,w,t'), 
                              min_{t'' in [t,t')}rho(psi,w,t') rho(phi,w,t'')))         otherwise


% Future timed temporal operators
rho(eventually[a,b] phi,w,t) = -inf                                                     if t+a >= |w|
                               max_{t' in ([0,t] intersect [t+a,t+b])} rho(phi,w,t')    otherwise
rho(always[a,b] phi,w,t) = inf                                                          if t+a >= |w|
                           min_{t' in ([0,t] intersect [t+a,t+b])} rho(phi,w,t')        otherwise
rho(phi until[a,b] psi,w,t) = -inf                                                      if t+a >= |w|
                              max_{t' in ([0,t] intersect [t+a,t+b]}(min(rho(psi,w,t'), 
                              min_{t'' in [t,t')}rho(psi,w,t') rho(phi,w,t'')))         otherwise   

We define the robustness degree rho(phi,w) as rho(phi,w,0).

There are several important points to note about the above syntax and semantics:

• In the online monitoring mode, the library allows only bounded-future STL specifications, meaning that unbounded future operators always eventually and until cannot appear in the specification.
• The prev and next operators are valid only under the discrete-time interpretation of STL
• The unless operator is added as syntactic sugar - `phi unless[a,b] psi = always[0,b] phi or phi until[a,b] psi

We can see from the semantics of bounded-future STL that the direct evaluation of a formula phi at time t may depend on inputs at t'>t that have not arrived yet. The library monitors bounded-future STL formulas with a fixed delay. In order to compute rho(phi,w,t), the monitor waits for all inputs required to evaluate phi to become available before computing the robustness degree. This delay is fixed and depends on the specification. For instance, the specification always((req >= 3) -> eventually[0:2]always[0:3](gnt >= 3)is evaluated with delay 5 - the time needed to capture all inputs required for evaluating bounded eventually and always operators. We refer the reader to [3] for algorithmic details regarding monitoring with delay.

Usage

The API provides two monitoring classes:

• StlDiscreteTimeSpecification for discrete-time monitors
• StlDenseTimeSpecification for dense-time monitors

Both classes implement online and offline monitors:

• update method is used for online evaluation . evaluate method is used for offline evaluation

Example Usage

Discrete-time online monitor

import sys
import rtamt

def monitor():
    # # stl
    spec = rtamt.StlDiscreteTimeSpecification()
    spec.declare_var('a', 'float')
    spec.declare_var('b', 'float')
    spec.spec = 'eventually[0,1] (a >= b)'

    try:
        spec.parse()
        spec.pastify()
    except rtamt.RTAMTException as err:
        print('RTAMT Exception: {}'.format(err))
        sys.exit()

    rob = spec.update(0, [('a', 100.0), ('b', 20.0)])
    print('time=' + str(0) + ' rob=' + str(rob))

    rob = spec.update(1, [('a', -1.0), ('b', 2.0)])
    print('time=' + str(0) + ' rob=' + str(rob))

    rob = spec.update(2, [('a', -2.0), ('b', -10.0)])
    print('time=' + str(0) + ' rob=' + str(rob))

if __name__ == '__main__':
    monitor()

Dense-time online monitor

import sys
import rtamt

def monitor():
    a1 = [(0, 3), (3, 2)]
    b1 = [(0, 2), (2, 5), (4, 1), (7, -7)]

    a2 = [(5, 6), (6, -2), (8, 7), (11, -1)]
    b2 = [(10, 4)]

    a3 = [(13, -6), (15, 0)]
    b3 = [(15, 0)]

    # # stl
    spec = rtamt.StlDenseTimeSpecification()
    spec.name = 'STL dense-time specification'
    spec.declare_var('a', 'float')
    spec.spec = 'a>=2'
    try:
        spec.parse()
    except rtamt.RTAMTException as err:
        print('RTAMT Exception: {}'.format(err))
        sys.exit()

    rob = spec.update(['a', a1], ['b', b1])
    print('rob: ' + str(rob))

    rob = spec.update(['a', a2], ['b', b2])
    print('rob: ' + str(rob))

    rob = spec.update(['a', a3], ['b', b3])
    print('rob: ' + str(rob))

if __name__ == '__main__':
    monitor()

Dense-time Offline Monitor

import sys
import rtamt

def monitor():

    req = [[0.0, 0.0], [3.0, 6.0], [5.0, 0.0], [11.0, 0.0]]
    gnt = [[0.0, 0.0], [7.0, 6.0], [9.0, 0.0], [11.0, 0.0]]
    
    spec = rtamt.StlDenseTimeSpecification()
    spec.name = 'STL Dense-time Offline Monitor'
    spec.declare_var('req', 'float')
    spec.declare_var('gnt', 'float')
    spec.declare_var('out', 'float')
    spec.set_var_io_type('req', 'input')
    spec.set_var_io_type('gnt', 'output')
    spec.spec = 'out = always((req>=3) implies (eventually[0:5](gnt>=3)))'
    try:
        spec.parse()
    except rtamt.RTAMTException as err:
        print('RTAMT Exception: {}'.format(err))
        sys.exit()

    rob = spec.evaluate(['req', req], ['gnt', gnt])

    print('Robustness: {}'.format(rob))

if __name__ == '__main__':
    # Process arguments
    monitor()

Discrete-time Specifics

Working with time units and timing assumptions

The default unit in RTAMT is seconds, and the default expected period between two consecutive input samples is 1s with 10% tolerance.
The following program uses these default values to implicitly set up the monitor.
The specification intuitively states that whenever the req is above 3, eventually within 5s gnt also goes above 3.
The user feeds the monitor with values timestamped exactly 1s apart from each other. It follows that the periodic sampling assumption holds.

RTAMT counts how many times the periodic sampling assumption has been violated up to the moment of being invoked via the sampling_violation_counter member.
In this example, this violation obviously occurs 0 times.

# examples/documentation/time_units_1.py
import sys
import rtamt

def monitor():
    spec = rtamt.StlDiscreteTimeSpecification()
    spec.name = 'Bounded-response Request-Grant'

    spec.declare_var('req', 'float')
    spec.declare_var('gnt', 'float')
    spec.declare_var('out', 'float')

    spec.spec = 'out = (req>=3) implies (eventually[0:5](gnt>=3))'

    try:
        spec.parse()
        spec.update(0, [('req', 0.1), ('gnt', 0.3)])
        spec.update(1, [('req', 0.45), ('gnt', 0.12)])
        spec.update(2, [('req', 0.78), ('gnt', 0.18)])
        nb_violations = spec.sampling_violation_counter // nb_violations = 0
    except rtamt.RTAMTException as err:
        print('RTAMT Exception: {}'.format(err))
        sys.exit()

if __name__ == '__main__':
    # Process arguments
    monitor()
}

The same program, but with slightly different timestamps still reports 0 number of periodic sampling assumption violations. This is because the difference between all consecutive sampling timestamps remains within the (implicitly) specified 10% tolerance.

# examples/documentation/time_units_2.py
    ...
    spec.update(0, [('req', 0.1), ('gnt', 0.3)])
    spec.update(1.02, [('req', 0.45), ('gnt', 0.12)])
    spec.update(1.98, [('req', 0.78), ('gnt', 0.18)])
    nb_violations = spec.sampling_violation_counter // nb_violations = 0
    ....

On the other hand, the following sequence of inputs results in 1 reported violation of periodic sampling assumption. This is because the third input is 1.12s away from the second sample, which is 12% above the assumed 1s period.

# examples/documentation/time_units_3.py
    ...
    spec.update(0, [('req', 0.1), ('gnt', 0.3)])
    spec.update(1.02, [('req', 0.45), ('gnt', 0.12)])
    spec.update(2.14, [('req', 0.78), ('gnt', 0.18)])
    nb_violations = spec.sampling_violation_counter // nb_violations = 1

This same sequence of inputs results in 0 reported violation of periodic sampling assumption if we explicitly set the sampling period tolerance value to 20%.

# examples/documentation/time_units_4.py
    ...
    spec.set_sampling_period(1, 's', 0.2)
    ...
    spec.update(0, [('req', 0.1), ('gnt', 0.3)])
    spec.update(1.02, [('req', 0.45), ('gnt', 0.12)])
    spec.update(2.14, [('req', 0.78), ('gnt', 0.18)])
    nb_violations = spec.sampling_violation_counter // nb_violations = 0

The user can also explicitly set the default unit, as well as the expected period and tolerance. In that case, the user must ensure that the timing bounds declared in the specification are divisible by the sampling period. The following specification is correct, since the sampling period is set to 500ms, the default unit is set to seconds, and the specification implicitly defines the bound from 0.5s = 500ms and 1.5s = 1500ms, i.e. between 1 amd 3 sampling periods.

# examples/documentation/time_units_5.py
    ...
    spec.unit = 's'
    spec.set_sampling_period(500, 'ms', 0.1)
    ...
    spec.spec = 'out = (req>=3) implies (eventually[0.5:1.5](gnt>=3))'
    ...
    spec.update(0, [('req', 0.1), ('gnt', 0.3)])
    spec.update(0.5, [('req', 0.45), ('gnt', 0.12)])
    spec.update(1, [('req', 0.78), ('gnt', 0.18)])
    nb_violations = spec.sampling_violation_counter // nb_violations = 0
}

The following defines the same program, but now with ms as the default unit.

 # examples/documentation/time_units_6.py
    ...
    spec.unit = 'ms'
    spec.set_sampling_period(500, 'ms', 0.1)
    ...
    spec.spec = 'out = (req>=3) implies (eventually[500:1500](gnt>=3))'
    ...
    spec.update(0, [('req', 0.1), ('gnt', 0.3)])
    spec.update(500, [('req', 0.45), ('gnt', 0.12)])
    spec.update(1000, [('req', 0.78), ('gnt', 0.18)])
    nb_violations = spec.sampling_violation_counter // nb_violations = 0
}

The following program throws an exception - the temporal bound is defined between 500ms and 1500ms, while the sampling period equals to 1s = 1000ms.

# examples/documentation/time_units_7.py
    ...
    spec.unit = 'ms'
    spec.set_sampling_period(1, 's', 0.1)
    ...
    spec.spec = 'out = always((req>=3) implies (eventually[500:1500](gnt>=3)))'
    ...
    spec.parse()
    ...
    
}

Finally, the following program is correct, because the temporal bound is explicitly defined between 500s and 1500s, while the sampling period equals to 1s.

# examples/documentation/time_units_8.py
    ...
    spec.unit = 'ms'
    spec.set_sampling_period(1, 's', 0.1)
    ...
    spec.spec = 'out = always((req>=3) implies (eventually[500s:1500s](gnt>=3)))'
    ...
    spec.parse()
    ...

References

• [1] Tomoya Yamaguchi, Bardh Hoxha, Dejan Nickovic: RTAMT - Runtime Robustness Monitors with Application to CPS and Robotics. International Journal on Software Tools for Technology Transfer, 1-21 (2023)
• [2] Dejan Nickovic, Tomoya Yamaguchi: RTAMT: Online Robustness Monitors from STL. CoRR abs/2005.11827 (2020)
• [3] Stefan Jaksic, Ezio Bartocci, Radu Grosu, Reinhard Kloibhofer, Thang Nguyen, Dejan Nickovic: From signal temporal logic to FPGA monitors. MEMOCODE 2015: 218-227
• [4] Thomas Ferrère, Dejan Nickovic, Alexandre Donzé, Hisahiro Ito, James Kapinski: Interface-aware signal temporal logic. HSCC 2019: 57-66
• [5] Thomas A. Henzinger, Zohar Manna, Amir Pnueli: What Good Are Digital Clocks? ICALP 1992: 545-558